If I'm lucky enough to catch a block with this local computer, how is it going to appear on both this local computer's wallet and the remote computer's wallet? Will I be able to distinguish coins coming from this computer's mining on the other end? Will I see anything at all in the transactions of the local computer's wallet? Is setting things up like this going to work at all? Will this work only up to the fork?
I'll spare everyone the conversation loop about a miner where you can see what is going on as we've done that one before.
Yes, it'll appear as a mined block on both.
No, unless you check the logs to see which mined the block.
Yes, on both as a mined transaction.
Yes.
No, it'll work before and after.