I don't know what you mean by this. I have games installed that i got for free with PS Plus that i downloaded 2-3 years ago and they still work. Some even kept working for a while after my subscription expired.
No they didn't. If you add days to a subscription while you have an existing one then games downloaded prior to the added days may say 'expired' when they reach the original date (before added days), but playing them again will make the display change to real days remaining.
If a subscription expires for real then it expires and no games will work.