Do you need to be a werewolf to complete the Companions quests

No, these quests do not end. These are simply due to the Radiant A.I., and never ending quests.

Also, as the Harbinger, you're not the leader, it would be better described as an adviser to the council of Companions.

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).