My site has many different "products". many are free types of membership, many are paid. Some of the products both free and paid have to be manually checked and approved first. (many others dont need to be checked) Is there any way I can get a separate email or notification sent when these certain products, that require manual approval, and registered?
No by default. You can enable manually approve invoices depends on purchased product (aMember CP -> Setup -> Advanced -> Manually Approve Invoices) but email notification is the same for all products.