Ok i had a look at the code. To fix your problems you need to look at the following. I tested it om my side and it works.

------------------------------------------------------
Konzert.php
-------------------------------------------------------

class Konzert extends DataObject {
   static $db=array(
      'KonzertName'=>'Varchar(150)',
      'DoorsOpen'=>'Varchar(150)'
      );
   static $has_one = array(
   // Left side is the name of relationship --- right hand side is the class is related to. This has_one relationship creates a column called
   // BandsID in our Konzert table to show Silverstripe that there is a relationship between the two classes
   'Bands'=>'Band'
   );

   // Sets the sumary fields that will be displayed in the grid field
   static $summary_fields = array(
'KonzertName',
    'DoorsOpen'
    );
   
   function getCMSFields() {   
   // to populate drowp down field for 'Band' it needs a source. We then 'map' the 'ID' col as the the one used to store values in database
   // and 'Name' is the name of the band ---- see code for 'Band.php'
   $BandDropdown = Dataobject::get("Band")->map("ID", "Name");

   // create new field list and remember we need to add our has_one field 'Band' in as well
   $fields = new FieldList (   
   
   new TextField('KonzertName', 'Name of the Konzert'),
   new TextField('DoorsOpen', 'Doors Open'),
   // The drop down field has 4 parameters:
      // 1) Name of the field that we are saving to. In our case it is has one relationship called 'Bands' that created a <br />
// field called BandsID in the table called Konzeret.
      // 2) The description 'Bands Playing'
      // 3) The values we want in our drop down menu we created above
      // 4) We leave params 4 and 5 open and set the deefault message for the drop down to 'Please select'
   new DropdownField('BandsID', 'Bands Playing', $BandDropdown,'','','--Please Select--')
   );
   return $fields;
   }
   
   // Now we set validation for our Data Object Fields
   public function getCMSValidator() {
return new RequiredFields(
   'KonzertName',
   // Remember our drop down field references the has_one relationship with the field BandsID
   'BandsID',
   'DoorsOpen'
   );
}
}

---------------------------------------------------
Band.php
----------------------------------------------------

class Band extends DataObject {
   static $db=array(
      'Name'=>'Varchar(150)'

      );

   function getCMSFields() {
   $fields = new FieldList (                  
   new TextField('Name', 'Band Name')
   );
   return $fields;
   }
   
}