Highly suggest you to go through some training first so you can get yourself acquainted with running affiliate offers on FB. There are certain niches that are banned by FB so make sure to read the advertising terms first!
Yes, You can promote Affiliate products facebook with both free and paid campaign. you have to know about how to work with paid campaign before you setup your campaign. at first study your niche and know your audience for promotion.
Yes You can post your affiliate link on your facebook page thru postings.
Also you can boost your posts and earn very good income by targeting
Also Search HTML App in your facebook search bar and install 3rd party
App in your facebook. You can show your ads on there.