Yes but your other computer on the LAN is connected to the network so it'll see you already spent your coins.
If disconnect both, in order to get a longer blockchain, you'll have to generate blocks; good luck with that.
BTC difficulty is currently 19,339,258.
You'd need to have 51% of the hashing power, hence why it's called the 51% attack.
You kinda left that step out.
You're right - don't turn on the slave system until you've disconnected the internet. The client will sync with your main system. (just add connect=192.168.x.x to the config)
EDIT: 51% attack implies 51% of the hashing power. Sorry for not making this even more brainless.