1. Must I create and maintain a pay-subscription with Apple?
You will need a personal Apple ID account, with a linked payment method, to use Apple services, like accessing the iTunes Store catalog of movies (and TV shows, depending on country). You do not need to subscribe to Apple TV+ or anything else. The iTunes Store movie catalog is separate from subscriptions.
2. Would Apple provide the video quality upgrades (e.g., HD to UHD) without paying for a subscription?
No subscription is involved. If you buy an eligible movie from the iTunes Store in HD that is later upgraded to 4K, HDR, Dolby Vision, or Dolby Atmos, you might not be able to watch the matching higher-quality version through a Movies Anywhere reciprocal service (but you will still be able to watch the HD version).
Apple no longer has the support page on M.A. [Internet Archive]. Instead Apple will refer to M.A. for details and terms.
3. If a pay-subscription is required, would I lose access to my movies if I end the subscription?
In the given context, no subscription is involved from Apple; it is about buy-content. But in general, if you subscribe, then the perks of that subscription end when you cancel that subscription.