1. is it "YOUR" site or will you be an affiliate?
2. Do you have a landing page or will you be direct linking?
3. Yes, it is allowed but you their are guidelines you need to follow.
You can build a landing page with good content or review and also have an opt in box to start to build your list.
The best way however, is to build a good Facebook page around the product and promote your page, not the landing page itself. make sure to have good relevant post on your page and keep your customers engaged. then you can sprinkle offers to the product over time and get them to buy.
You can also look into creating opt in forms and landing pages for your Facebook page, I have never done this but heard good things about.
Ryan