I have successfully started application but then it should have list of servers it must connect but it is empty and the only errors in terminal are those:
Install the latest wine, 1.4-rc2, soon 1.4-rc3, if you haven't already.
You are trying to (ab)use a .desktop file in the style of a perl script, this isn't what these files are intended for, afair windows .lnk files can be used in that way. Please run the actual commands hidden in your .desktop file and post terminal output again.
Did you install windows ODBC drivers or are you relying on wine's ODBC? Did you have a look at http://wiki.winehq.org/NativeOdbc ? In general, ODBC on wine may have some limits, if it still shouldn't work, you should file a bug and provide a simple testcase.
Installed NativeOdbc with winetricks and now application starts without fixme warning and showing 1 DB connection which is wrong instead of 4 that should be there. Any clue?
There's some advice on the wiki page about how to configure DSNs. Unfortunately I can't help you in that regard. As I said before, if it still doesn't work, please file a bug with a small demo, if possible. Similar topics were discussed before on that list, I told people to file bugs, but afaict no one did, probably people were thinking it would be too much work, and the prospect of waiting weeks or months until the issue gets fixed disappointed them. I understand that it isn't that easy, because you need a (publicly accessable) server or maybe some MS ACCESS file do demonstrate the issue. But if noone files a bug, the issue will never be solved.