mgranit
Sounds like URL Rewriting is not enabled on your webserver. The /api/tickets.json route for example gets captured by the rewrite rules (shipped with the software) and should be rewritten to /api/http.php/tickets.json. If URL Rewriting is not enabled or not working then it won't work.
If you can't or don't know how to enable URL Rewriting you can change the route to /api/http.php/tickets.json in your calls as a temporary workaround.
Cheers.
