Regarding F card of Belgium

If you keep your F-card you will pay tax in Belgium. If someone else has since registered at your old address your F-card will be cancelled anyway unless you have registered at a new residential address in Belgium.

Another person registered at your address will not cancel the registration of the first person registered, it will simply mean 2 menages registered to the same address. I experienced it myself, when I started getting letters for the previous occupants of my house, turned out 11 people were registered in 2 menages, the previous family left Belgium without deregistration, but I pointed out how Google found them back in their original country.

Yes if you go live outside Belgium, life will eventually catch up with you. No you cannot register f card outside Belgium. F+ card holders can leave Belgium for a maximum of 5 years and regain residency without starting recognition of EU family membership., not f card holders.