wolfET is the same thing.
azureus is what you need.
http://azureus.sf.net
there should be some documentation about how to symlink java to it and to mozilla and stuff. if it didnt already come with your distro.
its for all platforms.
so answer your question about doom running faster in linux than in windows - no.
windows was slightly faster last time i played doom in both OSes
but hl2 runs faster in Cedega (winex) than in windows.