Hi,
Is your 1st question also about the
Facebook Business Addon?
If it is related to the Addon, then no, you don't need to post all your products to your fanpage (If that is what you were asking)
What the Facebook Business Addon does, is to create a catalog of your store products, that you can then upload to your Facebook add account, it will also allow you to set automatic updates, plus it is compatible with WooCommerce too.
And yes, you will need an ad account for it, because you need to upload that catalog to your Facebook ad account. It could be a personal ad account, o a business one:
Facebook Ads Manager: Personal Account
https://www.facebook.com/adsmanager/
Facebook Business Manager:
https://business.facebook.com/
The reason for this, is because you need to create a paid campaign inside Facebook, to promote that catalog to your audience or store visitors. You can check this guide, which explains the process step by step:
Facebook Business Addon Guide