Hi Juraj,
just to update you... I can't let things rest... lol... so I recreated the solution from beginning going step by step... by doing that it just occurred to me how important the Multicultural handler is. I had the handler at the bottom of the default route with culture but not under the {pageAlias} one. As the handler addresses route as such rather than specific route, I have assumed that I didn't need it under every single route. Lesson learned... forever. :-) As for the other issues, they were caused by our security policies. Not running all scripts e.t.c. So we are now fully functional with only published files on the server and both the page and admin hooked up to IIS as separate sites and working fine.
Thanks a lot for bearing with me.
L.