Just in case there will be some time a XMR Classic fork ...
Are there any technical solutions in the protocol to prevent replay-attacks after a hard fork?
Is there any possibility to distinguish whether a receiver’s address is on an old chain or the most current chain with the most hash rate and greatest block height?
What happens with a transaction is sent to non-valid address?
1) The blockchain can fork at any time. From what I've observed, it only gets as far as 1-2 blocks down a branch before a chain reorganization occurs and the canonical longest branch is restored. Meanwhile, as noted here Why does Monero prevent transactions from being spent without 10 confirmations? it takes 10 blocks before any output is spendable. I believe this is the mechanism that you're asking for.
2) Wallet addresses are their own separate entity, they aren't dependent on a particular chain.
3) Non-valid addresses (with an invalid checksum) are rejected.
