Welcome to the Q&A Forum

hello, you can manage as many sites under 1 account as you want. there won't be any problem.

Hmm, it sounds very fishy eh. They won't build equity into your site, they want to build a site they control, they are spreading disinformation about ranking tools. To me, this is a just a small step away from: Give me your lunch money or I will beat you up! Not cool. Marcus

The one thing I would check with is making sure that your contest follows the rules of FB for a contest. The last thing you want to do is bring more attention to it and then discover that it's against FB's rules.

I would not spend one moment checking the authority of my pages. Not one moment. Instead, spend that time getting generous product descriptions on those pages and create great images to display the product.  All of those words will pull traffic from search on long tail queries.   They will show google that you have a substantive site.   They will inform the customer about your product and help make a buying decision.   The images will help sell the product and reduce the number of product questions that you receive. Creating a great site with great content is what produces results.  Page authority produces nothing.   It is possible to develop huge page authority but be completely ineffective at the goals of your website. Create pages and sites that serve your intended visitors.