Default keydefinitions for arrowkeys are "Seek forward" and "Seek backward".
Default keycombs for "Rewind" resp. "Fast forward" are [Ctrl]/[F6] resp.[Ctrl]/[F5].
Default key for full screen switch indeed is double left mouseclick (and/or depressing [F]-key)
(
This post also refers to these functions)
It seems someone(/something?) may have (accidentally?) changed keydefinitions of your BS.Player.
You can verify settings under
(rightclick >) Options > Preferences > Keydefinitions & WinLIRC
Pse note settings for 'Windowed mode' and ''Full screen mode' may be different, so to be sure for both modes, you have to verify both.