What happens if someone who sets, for example, 20 years from today's date but they don't die? Is it possible to cancel this transaction?
Yes, you'd just have to sign and broadcast a transaction emptying that address or moving them to the same address and renewing the transaction again. I'd assumed you'd end up with a more favourable transaction though at that point (eg you get more funds).
What if someone who sets it for 5 years later date or block, dies in a year or two? Is there any possibility for their known family member to get these coins before the set "LockTime" period by any means or they need to wait for 5 years before they are sent the coins to their address?
Yes if you left your mnemonic phrase or private key in a place they could easily find... Which is possible if you trust them or you'll know they'll look in a certain place. But I don't think this is a bad backup in case a physical store gets destroyed as well...