Calculating differences in time from multiple rows

Question 1

with orderedTickets as 
(
    select ShopOrder, min(StartDateTime) as date 
         , row_number() over (order by min(StartDateTime)) as rownumber
    from table 
    where ShopOrder is not null  
    group by ShopOrder
)
select t1.ShopOrder, datediff(ss, t1.StartDateTime, t2.StartDateTime) 
  from orderedTickets as t1 
  join orderedTickets as t2 
    on t2.rownumber = t1.rownumber + 1

Question 2

Here is a solution to the first problem, which is getting the next date time on the "next" shop order. This solution uses a correlated subquery:

select t.*, nextStartDateTime - StartDateTime -- or use datediff() here if you want the time in particular units
from (select t.*,
             (select top 1 StartDateTime
              from t t2
              where t2.StartDateTime > t.StartDateTime and
                    t2.ShopOrder <> t.ShopOrder
              order by StartDateTime
             ) as nextStartDateTime
      from t
     ) t;

The second problem is getting the first record for a given shop order. I'm not sure I understand this fully. It would help if you edited the question to explain the results that you want on the data provided in the question.

Question 3

Use CTE, -

;with Equipment as 
(
select EquipmentUseId, CollectionPointId, EmployeeNum, ShopOrder, StartDateTime, row_number() over (PARTITION BY ShopOrder order by EquipmentUseId) as rownumber
from your_table 
),
Equipment2 AS (
select EquipmentUseId, CollectionPointId, EmployeeNum, ShopOrder, StartDateTime, row_number() over (order by EquipmentUseId) as rownumber
from Equipment WHERE rownumber = 1
)

SELECT t1.EquipmentUseId,
   t1.CollectionPointId,
   t1.EmployeeNum,
   t1.ShopOrder,
   t1.StartDateTime,
   CONVERT(VARCHAR, DATEDIFF(n, t1.StartDateTime, t2.StartDateTime) / 60) + ':' +  RIGHT('0' + CONVERT(VARCHAR,(DATEDIFF(n, t1.StartDateTime, t2.StartDateTime)%60)), 2) time_diff
FROM   Equipment2 AS t1
LEFT JOIN Equipment2 AS t2 ON  t2.rownumber = t1.rownumber + 1