I managed to solve both the problems.
The first problem (getting the DirectShow not installed 00xx error) was due to BSPlayer's automatic codec installer manager. I got rid of the problem by uninstalling BSP and removing
C:\Program Files\Webteh folder, then installing BSP and not allowing it to automatically download codecs. The problem appears if I allow it to install any of this codecs : FFDShow, MPEG 2 video codec, Real media spliter, Haali splitter.
The second problem was that BSP could not associate with files and wouldn't show up in "Open with" menu, even when browsed for. I solved this problem by finding this site
Registering programs with the "Open With" dialog
and downloading the application. Then I just ran it, browsed to C:\Program Files\Webteh\BSplayer\bsplayer.exe, clicked "Register" and everything worked again.
I post the solutions here in hope I could help someone else.