Can I play LAN?
Well LAN isn't essential. If I get an extra copy of Minecraft will me and my brother be able to share a world, save, quit and return to it later.
Basically like normal singleplayer survival mode, plus one person.
Yes
Yes of course, you still need to have the server software running on one of the 2 computers, but you will still be able to play from the same network without port forwarding.
WoM Coins: 8985
Yes, I'm sure there is an option with the server software from the website Minecraft.net to join a server just for a LAN network. If I wasn't at school I would go look it up for you but it is there. I'm sure you just run the software and connect with a LAN ip such as 192.1.1.2.