Do I get reimbursed by Epic Games for everyone who downloads my product while it’s Free for the Month or not.
No, you’re not reimbursed for each download. If your product is selected, you get one time payment of up to $5,000 (USD) and will vary depending on the selected product.
How does it work? Do they choose my product at random for the feature or do they ask if I want to feature it in “Free for the month”?
In order to be eligible you have to apply here: Free Content Submission
As far as I know, if they choose your product, they contact you in advance for all the necessary bureaucracy.