In Skyrim, are the Companion quests still available after taking over Whiterun (Stormcloaks path)?

You can still finish the quests for the Companions - joining the Stormcloaks and taking Whiterun actually has very little impact on practical gameplay, as it mostly just replaces some NPCs with some other NPCs, and some NPCs become happier than some others.

As for the second part of your question, you'll be able to cure yourself of lycanthropy as well, in the same manner that everyone else cures it (if you need a bit of help there, check this question out).