How to use preceding-sibling to check previous xpath element

Question 1

It's a bit tricky to give a precise answer without seeing a sample of your expected HTML, and also because the element names in your XSLT don't seem to match up with your input XML sample. However, the technique you need to be reading up about and using here is Muenchian Grouping. This is the most efficient way of grouping elements in XSLT 1.0.

In your case, you want to get the distinct journeys for the passenger, and then get the first segment for each one. You do this by defining a key to lookup the passengersegment elements by their journeynumber

<xsl:key name="journey" match="passengersegment" use="journeynumber"/>

Then, to get the distinct journey numbers, you look at all passengersegment but only select the ones that occur first in the key for their given journeynumber value.

<xsl:apply-templates 
     select="passengersegment
             [generate-id() = generate-id(key('journey', journeynumber)[1])]"/>

Within the template that matches passengersegment you can then output the first carryonbagcount and checkednbagcount for the segment (the first in the journey).

Try this XSLT as a start, and build on this:

<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
  <xsl:output omit-xml-declaration="yes" indent="yes"/>
  <xsl:key name="journey" match="passengersegment" use="journeynumber"/>

  <xsl:template match="/passenger">
    <table border="1">
      <tr>
        <th>Journey</th>
        <th>Carry on</th>
        <th>Checked</th>
      </tr>
      <xsl:apply-templates select="passengersegment[generate-id() = generate-id(key('journey', journeynumber)[1])]"/>
    </table>
  </xsl:template>

  <xsl:template match="passengersegment">
    <tr>
      <td>
        <xsl:value-of select="journeynumber"/>
      </td>
      <td>
        <xsl:value-of select="carryonbagcount"/>
      </td>
      <td>
        <xsl:value-of select="checkedbagcount"/>
      </td>
    </tr>
  </xsl:template>
</xsl:stylesheet>

Note that if wanted to get the total carryonbagcount for all segments in the journey, then within the passengersegment you could do something like this:

<xsl:value-of select="sum(key('journey', journeynumber)/carryonbagcount)" />

Question 2

Assuming that the output carryonbagcount should be the maximum of each of the legs, here is a small tweak to Tim's answer.

This input document...

<passenger>
  <passengersegment>
      <journeynumber>0</journeynumber>
      <segmentnumber>0</segmentnumber>
      <carryonbagcount>1</carryonbagcount>
      <checkedbagcount>1</checkedbagcount>
  </passengersegment>
  <passengersegment>
       <journeynumber>0</journeynumber>
       <segmentnumber>1</segmentnumber>
       <carryonbagcount>1</carryonbagcount>
       <checkedbagcount>1</checkedbagcount>
   </passengersegment>
   <passengersegment>
       <journeynumber>1</journeynumber>
       <segmentnumber>0</segmentnumber>
       <carryonbagcount>1</carryonbagcount>
       <checkedbagcount>1</checkedbagcount>
   </passengersegment>
   <passengersegment>
       <journeynumber>1</journeynumber>
       <segmentnumber>1</segmentnumber>
       <carryonbagcount>1</carryonbagcount>
       <checkedbagcount>1</checkedbagcount>
   </passengersegment>

... when this XSLT 1.0 stylesheet is applied to it ...

<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" version="2.0">
<xsl:output method="html" doctype-system="about:legacy-compat" encoding="UTF-8" indent="yes" />
<xsl:strip-space elements="*" />

<xsl:key name="kJourney" match="passengersegment" use="journeynumber" />  

<xsl:template match="/*">
<table>
 <thead>
  <tr>
   <th><strong>Journey</strong></th> <th><strong>CARRY-ON</strong></th> <th><strong>CHECKED</strong></th>
  </tr>
 </thead>
 <tbody>
    <xsl:apply-templates select="passengersegment[generate-id() =
                                                  generate-id(key('kJourney',journeynumber)[1])]"
                         mode="group" /> 
 </tbody>
</table>
</xsl:template>

<xsl:template match="passengersegment" mode="group">
  <tr>
    <td><xsl:value-of select="journeynumber" /></td>

    <xsl:apply-templates select="." mode="max"> 
      <xsl:with-param name="col-name" select="'carryonbagcount'" />
    </xsl:apply-templates>

    <xsl:apply-templates select="." mode="max"> 
      <xsl:with-param name="col-name" select="'checkedbagcount'" />
    </xsl:apply-templates>
  </tr>  
</xsl:template>

<xsl:template match="passengersegment" mode="max"> 
  <xsl:param name="col-name" /> 
  <xsl:for-each select="key('kJourney',journeynumber)/*[name()=$col-name]">
    <xsl:sort select="." data-type="number" order="descending" />
    <xsl:if test="position()=1">
      <td><xsl:value-of select="." /></td>
    </xsl:if>
  </xsl:for-each>  
</xsl:template>  

</xsl:stylesheet>

...yields this HTML output...

<!DOCTYPE html SYSTEM "about:legacy-compat">
<table>
  <thead>
    <tr>
      <th><strong>Journey</strong></th>
      <th><strong>CARRY-ON</strong></th>
      <th><strong>CHECKED</strong></th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>0</td>
      <td>1</td>
      <td>1</td>
    </tr>
    <tr>
      <td>1</td>
      <td>1</td>
      <td>1</td>
    </tr>
  </tbody>
</table>

Update

The OP has altered the question and sample data so far, it is really a new question. Assuming that the @entity_id uniquely identifies a passenger. If not, the OP should properly explain the input data structure and rules of transformation. So here is a solution to the new question..

This XSLT 1.0 stylesheet...

<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" version="2.0">
<xsl:output method="html" doctype-system="about:legacy-compat" encoding="UTF-8" indent="yes" />
<xsl:strip-space elements="*" />

<xsl:key name="kJourney" match="passseg_to_passenger"
  use="concat( ../../Prop/@entity_id, '|', Prop[@prop_name='journeynumber']/@val)" /> 
  <!-- Assume that @entity_id is an identifier for the passenger. -->

<xsl:template match="bookingcontact_to_booking">
<table>
 <thead>
  <tr>
   <th><strong>PASSENGER</strong></th> <th><strong>CARRY-ON</strong></th> <th><strong>CHECKED</strong></th>
  </tr>
 </thead>
 <tbody>
   <xsl:apply-templates select="passenger_to_bookings/passenger_to_booking" /> 
 </tbody>
</table>
</xsl:template>

<xsl:template match="passenger_to_booking">
  <xsl:variable name="passenger-id" select="(Prop/@entity_id)[1]" />
  <xsl:variable name="passenger-name" select="
   concat( Prop[@prop_name='firstname']/@val, ' ', Prop[@prop_name='lastname']/@val)" />
  <tr>
   <xsl:apply-templates select="passseg_to_passengers/passseg_to_passenger
       [generate-id() = generate-id(key('kJourney',
            concat( $passenger-id, '|', Prop[@prop_name='journeynumber']/@val))[1])]"
     mode="group"> 
    <xsl:with-param name="passenger-id"   select="$passenger-id" />
    <xsl:with-param name="passenger-name" select="$passenger-name" />
  </xsl:apply-templates>   
  </tr>
</xsl:template>

<xsl:template match="passseg_to_passenger" mode="group">
  <xsl:param name="passenger-id" />
  <xsl:param name="passenger-name" />
  <td><xsl:value-of select="$passenger-name" /></td>

  <xsl:apply-templates select="." mode="max"> 
    <xsl:with-param name="passenger-id" select="$passenger-id" />
    <xsl:with-param name="col-name" select="'carryonbagcount'" />
  </xsl:apply-templates>

  <xsl:apply-templates select="." mode="max"> 
    <xsl:with-param name="passenger-id" select="$passenger-id" />
    <xsl:with-param name="col-name" select="'checkedbagcount'" />
  </xsl:apply-templates>
</xsl:template>

<xsl:template match="passseg_to_passenger" mode="max"> 
  <xsl:param name="passenger-id" />
  <xsl:param name="col-name" /> 
  <xsl:for-each select="key('kJourney',
      concat( $passenger-id, '|', Prop[@prop_name='journeynumber']/@val)
  )/Prop[@prop_name=$col-name]/@val">
    <xsl:sort select="." data-type="number" order="descending" />
    <xsl:if test="position()=1">
      <td><xsl:value-of select="." /></td>
    </xsl:if>
  </xsl:for-each>  
</xsl:template>  

</xsl:stylesheet>

...when applied to this input document...

<bookingcontact_to_booking>
    <passenger_to_bookings> 
        <passenger_to_booking>
            <Prop pk_id="4147" entity_id="126" val="SMITH" type_id="20" prop_name="lastname" prop_id="10208"/>
            <Prop pk_id="4147" entity_id="126" val="PEDRO" type_id="20" prop_name="firstname" prop_id="10206"/>
            <passseg_to_passengers>
                <passseg_to_passenger>
                    <Prop pk_id="9432" entity_id="122" val="2013-08-27 17:45:00.000" type_id="30" prop_name="arrivaltime" prop_id="10216"/>
                    <Prop pk_id="9432" entity_id="122" val="188" type_id="20" prop_name="flightnumber" prop_id="10217"/>
                    <Prop pk_id="9432" entity_id="122" val="5" type_id="10" prop_name="checkedbagcount" prop_id="10220"/>
                    <Prop pk_id="9432" entity_id="122" val="1" type_id="10" prop_name="carryonbagcount" prop_id="10221"/>
                    <Prop pk_id="9432" entity_id="122" val="1" type_id="10" prop_name="journeynumber" prop_id="10222"/>
                    <Prop pk_id="9432" entity_id="122" val="0" type_id="10" prop_name="segmentnumber" prop_id="10223"/>
                    <Prop pk_id="9432" entity_id="122" val="2013-08-27 08:12:00.000" type_id="30" prop_name="departuretime" prop_id="10296"/>
                    <Prop pk_id="9432" entity_id="122" val="Las Vegas, NV" type_id="20" prop_name="departureairport" prop_id="10297"/>
                    <Prop pk_id="9432" entity_id="122" val="New York, NY - LaGuardia " type_id="20" prop_name="arrivalairport" prop_id="10298"/>
                    <Prop pk_id="9432" entity_id="122" val="10B,20B" type_id="20" prop_name="seatassignment" prop_id="10299"/>
                </passseg_to_passenger>
                <passseg_to_passenger>
                    <Prop pk_id="9433" entity_id="122" val="10B,20B" type_id="20" prop_name="seatassignment" prop_id="10299"/>
                    <Prop pk_id="9433" entity_id="122" val="Fort Lauderdale, FL" type_id="20" prop_name="arrivalairport" prop_id="10298"/>
                    <Prop pk_id="9433" entity_id="122" val="New York, NY - LaGuardia " type_id="20" prop_name="departureairport" prop_id="10297"/>
                    <Prop pk_id="9433" entity_id="122" val="2013-08-27 19:45:00.000" type_id="30" prop_name="departuretime" prop_id="10296"/>
                    <Prop pk_id="9433" entity_id="122" val="1" type_id="10" prop_name="segmentnumber" prop_id="10223"/>
                    <Prop pk_id="9433" entity_id="122" val="1" type_id="10" prop_name="journeynumber" prop_id="10222"/>
                    <Prop pk_id="9433" entity_id="122" val="1" type_id="10" prop_name="carryonbagcount" prop_id="10221"/>
                    <Prop pk_id="9433" entity_id="122" val="5" type_id="10" prop_name="checkedbagcount" prop_id="10220"/>
                    <Prop pk_id="9433" entity_id="122" val="779" type_id="20" prop_name="flightnumber" prop_id="10217"/>
                    <Prop pk_id="9433" entity_id="122" val="2013-08-27 22:45:00.000" type_id="30" prop_name="arrivaltime" prop_id="10216"/>
                </passseg_to_passenger>
            </passseg_to_passengers>
        </passenger_to_booking>
    </passenger_to_bookings>
</bookingcontact_to_booking>

...yields this html output document...

<!DOCTYPE html SYSTEM "about:legacy-compat">
<table>
  <thead>
    <tr>
      <th><strong>PASSENGER</strong></th>
      <th><strong>CARRY-ON</strong></th>
      <th><strong>CHECKED</strong></th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>PEDRO SMITH</td>
      <td>1</td>
      <td>5</td>
    </tr>
  </tbody>
</table>