For facebook ads, are you allowed to just link your ads directly to your CPA offer? Or do you have to create your own website and put your offer in your website?

Yes, If your ad allows social traffic and that type of lead generation. or you can do the website thing and direct them there too. Your choice.

No!
Its against the FB terms of service.
The only case you can link,i guess, when your referral link and the landing page point to the same domain. thats it.

True. I guess I was just reffering to the CPA side of things. However, you can do a redirect etc, etc...probably just makes sense to point to your website with a pop-up or something...

I don't think you can do a redirect either....unless you have it set up so the url they clicked shows up. Both urls have to be identical if I'm not mistaken.