While adding a new product I get the error message "Please enter a valid email address". Why so?

For each portal on your account, you would have one dedicated primary email address associated with it. The main portal will have a similar primary support email and the product portal will have it's own distinct primary email address. 

Existing emails cannot be used while creating a new product. You would have to add a new/unique email address and associated it with the New Product which is being created.