I honestly have no idea what light clients will see. I guess it depends from where they pull their data.

As for transactions, a basic transaction will be valid on all chains, but when you move between your wallets nobody has an incentive to replay that, but it might still be replayed. But when you put one of the 'new' opcodes that will not be valid on all the chains. So there is a clear way to separate the coins.

Note that when you send coins on the SV chain to a new address, then your coins on BCH are protected when you send them. But when you send your SV coins to a merchant, the merchant can still replay your transaction. All they need to do is replay moving the BCH coins to your SV address and then repaying from there. So to be safe all coins on all chains need to go to a new different address.

There are indeed 3 forks, plus the ability to mine the old. Bitcoin ABC and Bitcoin SV are not compatible in the chain. Bitcoin unlimited should be compatible with both. Not forking is compatible with neither.
But in practice it may be a lot messier. As long as the new opcodes are not used and there are no huge blocks, everyone is compatible with everyone. Then if a new opcode is used on a low hash-power chain that block may end up being orphaned.

Will be exciting to see how this plays out.