Hi!

Yes you can do that! When you have already joined the Amazon Parner Program you can Build an AStore which you find on the Amazon Partner - Page. When everything is Set up you can integrate it on your Fanpage via iframe App. There are a few instruction videos on YT also. But if you have further Questions, PM me.

You're in the clear. Go for it! And while you're at it, get on Pinterest too! Viralwoot is great for promoting your pins for repinning.

Absolutely, I've seen it done many times.