Annoying solicitation messages

When I buy an apple product can I ask to have all subscription services turned off

You can leave the check boxes empty, in other words do not put a check mark.

so I don't get in app purchases requests from Apple?

App purchases requests that's something else.

If you are going to download a free app, there is a possibility to purchase the 'better' version, for example from free to pro.

But that is not mandatory.

However, with the Free version there is an advertisement.

Free App(s) -> do Offers In-App Purchases.