These competing blocks will be broadcast to the network and someone sending large amount should watch for a possible blockchain reorganization.
Still, though. Once the chain gets reorged, which happens usually for 1 block, the transactions of the block that was dumped, become unconfirmed and return to the mempool. Now they can get mined within the next blocks. If I was going to receive a lot of money, I'd ask to disable RBF and have at least 1 confirmation. Disabling RBF means you can't (practically) double-spend your unconfirmed transaction.
If my transaction has one or two confirmations and there are no competing blocks that don't have my transaction then I am pretty sure that my transaction went through.
That's true. Chain reorgs, as I've said, usually affect the last block. I don't believe it has ever happened for 2 or more.