Impossible to know. It would be best to keep yourself aware of any major new developments in Bitcoin if you are holding any bitcoin. In general, a paper wallet (if created in a safe manner) should be safe until mathematicians manage to completely break all three of ECDSA, SHA-256, and RIPEMD-160. I'll be surprised if all three of those are completely broken to the point of being reversible in less than a decade.
While not impossible, what would be more likely than that is for the current cryptography to become weakened with new mathematical developments. The bitcoin protocol would be updated with new cryptography, and your old paper wallet (while still supported by the new protocol) would become vulnerable to theft.
That wouldn't hurt, but it isn't likely to help. If the protocol changes in a way that makes it impossible to spend your bitcoins (extremely unlikely), then your old program won't be recognized as valid by the rest of the network.
Not usually. Usually, a paper wallet only has a single receiving address.
The single QR-Code will most likely hold enough information to recreate a single receiving address. If you want multiple receiving addresses, then each one will have it's own pair of QR-Codes.
The paper wallet is generally created separate from the digital one. It has its own address that doesn't eve exist in the digital wallet. You send the bitcoins from your digital wallet to the paper wallet. Therefore, there aren't any bitcoins in the digital wallet for anyone to steal. As such, there is no need to destroy the digital wallet. If it falls into the wrong hands it is useless (since it doesn't contain any of the bitcoins.
Deleting an empty wallet isn't a very difficult thing to do. Trusting that the paper wallet receiving address matches the paper wallet private key, and sending the bitcoins to the paper wallet receiving address can take some faith though.