If I try to create a link to another xwiki page I can search for the xwiki titles of the pages:
For some use case I created a template with a template class and some attributes. Is it possible to search for such an attribute when creating a link to a xwiki page of that template type via the wysiwyg editor?
No that's not possible from the WYSIWYG. You can use the wiki search to find the page name though.