1. Will CB integrate with the main component:

Depends on what you want to integrate. If you mean push CB data to that component then probably using CB Auto Actions and its Query or Code action would be sufficient.

2. Will CB Paid Subscription integrate will the listing pages:

Depends on what you want to integrate. If you mean have a CBSubs plan to purchase a listing then yes I suppose it could do that, but you'll need a plan per listing.

3. Is there a CB plugin for auction and bidding?

Nope.

4. Could we generate an invoice with CB for each payment received?

As long as you're using single payments instead of recurring payments a new basket is generated with every payment. A basket in CBSubs is basically an invoice. Recurring payments do not generate new baskets so no you won't have an invoice per payment in that case.