It will handle - the method begin () is your friend.
No it won't.
There is a library written specifically for the 40x4 displays. Start here: Google Code Archive - Long-term storage for Google Code Project Hosting.
Also - there's another method using two instances of the regular library mentioned here: 40x4 Display (FDCC4004A-FLYYBW-51SE, 2x ST7066U) - Displays - Arduino Forum
Don