In that instance, you'll have to remove your coins to a new wallet from the bip110 fork fist, since, unless I'm mistaken, that does have replay protection? Then the core side of tue fork will be unaffected. Do it the other way around and your bip110 coins will be gone.

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Yeah, if the transaction is replayed on the fork chain, and the transaction signs for a utxo that doesnt exist over there, it's an invalid transaction. But honestly, splitting coins for BIP-110 is a pretty stupid thing to do, since it likely won't even have a spot market before the miners abandon the effort. Lot of room for error with very little chance of reward.
No. On core chain you will have send transactions that have larger than 83byte OP_RETURNs to be sure the transaction isn’t replayed.