1. Will MAST allow complex Smart Contract or still only can use P2SH ?
I'm pretty sure MAST only permits a limited amount of extra complexity using the existing op-codes.
2. Since MAST can increase user privacy, i wonder if MAST also can increase privacy when user use LN (especially some users have concern if they let user use connect to other users through their channel and turned out it's criminal acitivity)?
MAST only increases privacy in specific circumstances; if a script has branches (e.g. when a threshold of signers is less than the total possible, 2 of 3 for instance), then only the branch that is satisfied ends up published on the blockchain when using MAST (e.g. if person 1 & 2 sign a transaction, person 3's pubkey isn't disclosed at all as a part of the transaction). With current scripting, all branches of a script are published when the script is spent from. This can make MAST transactions smaller than regular P2SH.
I don't think this will change LN privacy properties, it's already a private system in any case. I don't think it could make channel open/close transactions smaller, as they're always 2 of 2, but there's maybe some subtlety I've not picked up on.
3. GitHub page mentioned MAST will be soft fork, but i wonder how will the backward compatibility works, is it similar with backward compatibility that SegWit use?
There are no deployment implementations that I'm aware of, but any soft-fork is likely to get deployed using version bits (which Segwit was).
