Bitcoin block maturity and block reward rules
Split chains can be seen as separate coins, except that a transaction with inputs valid in both chains (maybe a coinbase before the fork) would be valid in both. In that miner's chain, the miner can spend his coinbase. The rest of the nodes will see the transaction as invalid and ignore it, as his block isn't part of the main chain. If the miner wants, the miner can advertise his chain as a "new coin", referencing the first block that is not common, and nodes who would be built to recognize his chain would allow the miner to spend the coinbase transaction.

In the second scenario, the same thing happens. What he does is well-received in his chain, but ignored in the main chain (the chain with the largest proof-of-work)