Google Maps API3 InfoWindow and query if Marker is in polygon or not

Question 1

there is a typo

   oogle.maps.event.addListener(marker, 'click', function() {
//^ missing a g

most of your variables are defined local in the scope of initialize, but codeAddress is defined in global scope and isn't able to access these variables
use the method google.maps.geometry.poly.containsLocation to detect if the marker is within a polygon(Note: you must include the geometry-library, it's not loaded by default)

fixed code(I've removed irrelevant stuff):

<script src="https://maps.googleapis.com/maps/api/js?v=3&sensor=false&language=ch&libraries=geometry"></script>
<script>
function initialize() {

  var geocoder      = new google.maps.Geocoder(),
      mapOptions    = { zoom: 8,
                        center: new google.maps.LatLng(46.8131873, 8.2242101)
                      },
      //use only a single marker
      marker        = new google.maps.Marker(),
      infowindow    = new google.maps.InfoWindow(),

      map           = new google.maps.Map(document.getElementById('map-canvas'), 
                                          mapOptions),
      //store the polygons in an array for iteration
      polys         = [];       
      polys[0]      = new google.maps.Polygon({
                        title:'Montagegebiet 1',
                        paths: [
                            new google.maps.LatLng(47.554615, 7.59446),
                            new google.maps.LatLng(47.377455, 8.536715),
                            new google.maps.LatLng(46.9546699, 7.39487),
                            new google.maps.LatLng(47.554615, 7.59446)
                          ],
                        map:map
                      });

      polys[1]      = new google.maps.Polygon({
                        title:'Montagegebiet 2',
                        paths: [
                            new google.maps.LatLng(46.74021, 7.638205),
                            new google.maps.LatLng(46.1731573, 8.7772588),
                            new google.maps.LatLng(47.04739, 8.3183349),
                            new google.maps.LatLng(46.74021, 7.638205)
                          ],
                         map:map
                      });


      google.maps.event.addListener(marker, 'click', function() {
        infowindow.open(map,marker);
      });

      //define the codeAdress-function in the scope of initialize
      //to be able to access all variables without declaring them global
      window.codeAddress  = function() {

        var address = document.getElementById('address').value;

        geocoder.geocode( { 'address': address}, function(results, status) {
          if (status == google.maps.GeocoderStatus.OK) {
            var position = results[0].geometry.location,
                //default-content for infowindow
                content  = 'Die Eingabe befindet sich in keinem der Bereiche';
            map.setCenter(position);

            marker.setOptions({
              map:map,
              animation: google.maps.Animation.DRPOP,
              position: position
            });

            for(var i=0;i<polys.length;++i){
              //check if the latLng is placed within the polygon
              if(google.maps.geometry.poly.containsLocation(position,polys[i])){
                //if it does, update the  content for the infowindow
                content = 'Die Eingabe wurde in '+polys[i].title+' lokalisiert';
                //and leave the loop
                break;
              }
            } 
            //open the infowindow
            infowindow.setOptions({
                  map:map,
                  position:position,
                  content:content
            });
          } 
          else {
            //hide the infowindow
            infowindow.setMap(null);
            alert('Die Eingabe lieferte kein Ergebnis');
          }
        });
      }
}

google.maps.event.addDomListener(window, 'load', initialize);

</script>

Demo: http://jsfiddle.net/doktormolle/nYebu/

Question 2

The code is working now, I wanted to have a InfoWindow which pops up if the Marker is set. It is working if I open the index.html File offline in my browser, bet when I use it in this "testing environment", the InfoWindow part wont work... Why is that?

http://irrturm.de/Montageservice/Index.html

Also if I try to implement my Google Maps API Key, there is a JavaScript Alert telling that my API Key is not valid, even though it should be valid since I created this:

Picture: http://s4.postimg.org/cszh2jad9/Screen_Shot_2014_03_31_at_10_16_12.png

<script>


//Deklarierung der Variablen
var geocoder;
var map;

//Initialisieren der Karte
google.maps.event.addDomListener(window, 'load', initialize);

//Schweiz als Kartenmitte anwählen 
function initialize() {
geocoder = new google.maps.Geocoder();

  var mapOptions = {
    zoom: 8,
    center: new google.maps.LatLng(46.8131873, 8.2242101),
   disableDefaultUI: false
  };

  var bermudaTriangle;
  var bermudaTriangle2;

//Deklarierung der neuen Google Maps Karte
  map = new google.maps.Map(document.getElementById('map-canvas'), mapOptions);


  //Algorithmus um rauszfinden ob Marker im Polygon ist oder nicht






  //Montagegebiet 1
    var triangleCoords = [
    new google.maps.LatLng(47.554615, 7.59446),
    new google.maps.LatLng(47.377455, 8.536715),
    new google.maps.LatLng(46.9546699, 7.39487),
    new google.maps.LatLng(47.554615, 7.59446)
  ];

  //Montagegebiet 2
    var triangleCoords2 = [
    new google.maps.LatLng(46.74021, 7.638205),
    new google.maps.LatLng(46.1731573, 8.7772588),
    new google.maps.LatLng(47.04739, 8.3183349),
    new google.maps.LatLng(46.74021, 7.638205)
  ];


  //Aussehen des Montagebiets
  bermudaTriangle = new google.maps.Polygon({
    paths: triangleCoords,
    strokeColor: '#4BC4DF',
    strokeOpacity: 0.8,
    strokeWeight: 2,
    fillColor: '#4BC4DF',
    fillOpacity: 0.35
  });

  //Aussehen des Montagegebiets 2
  bermudaTriangle2 = new google.maps.Polygon({
    paths: triangleCoords2,
    strokeColor: '#4BC4DF',
    strokeOpacity: 0.8,
    strokeWeight: 2,
    fillColor: '#4BC4DF',
    fillOpacity: 0.35
  });

//Setzen der Montagegebiete auf die Karte
  bermudaTriangle.setMap(map);
  bermudaTriangle2.setMap(map);
}


//ContentString1 (Montage möglich)
 var contentString = '<div id="content">'+
      '<div id="siteNotice">'+
      '</div>'+
      '<h1 id="firstHeading" class="firstHeading">Ihr Ort liegt im Montagegebiet</h1>'+
      '<div id="bodyContent">'+
      '<a href="http://glaswelt24.ch/Montage-Service:_:35.html">'+
      'Jetzt Montageservice buchen</a> '+
      '</div>'+
      '</div>';


 //Contentstring 2 (Montage nicht möglich)     
       var contentString2 = '<div id="content">'+
      '<div id="siteNotice">'+
      '</div>'+
      '<h1 id="firstHeading" class="firstHeading">Ihr Ort liegt im Montagegebiet</h1>'+
      '<div id="bodyContent">'+
      '<a href="http://glaswelt24.ch/Montage-Service:_:35.html">'+
      'Jetzt Montageservice buchen</a> '+
      '</div>'+
      '</div>';

//InfoWindow erstellen ohne Inhalt 
var infowindow = new google.maps.InfoWindow({
content: contentString
});

//InfoWindow2
var infowindow2 = new google.maps.InfoWindow({
content: contentString2
});


//Adresseingabe
function codeAddress() {
  var address = document.getElementById('address').value;
  geocoder.geocode( { 'address': address
   }, function(results, status) {
    if (status == google.maps.GeocoderStatus.OK) {
      map.setCenter(results[0].geometry.location);


      //Marker auf der Karte
          var marker = new google.maps.Marker({
          map: map,
          position: results[0].geometry.location,
          title: address,
          navigationControl: false,
    mapTypeControl: false,
    scaleControl: false,
    draggable: false
     });

    //Click-Event für den Marker
    infowindow.open(map,marker);

    google.maps.event.addListener(infowindow, 'closeclick', function () {
                        marker.setVisible(false);
                    });

 } else {


        infowindow2.open(map,marker);


    google.maps.event.addListener(infowindow2, 'closeclick', function () {
                        marker.setVisible(false);
                    });

    }

 });      



}

    </script>