Mechs and vehicles from the board/miniatures game?
It depends on what time period the game is in, but otherwise, yes. A Time of War is all about playing a finer scale of BT, so there's going to be a great deal of continuity between the two. The main difference is in how AToW notes target numbers for rolls.
Where is the Full Rulebook?
Battleforce or Drive-Thru RPG for a .pdf version. Hardcopy outlets like Amazon or a local game shop can furnish a printed version.
Where is the Marauder IIC statted up?
A variety of places. There's the original Tech Readout 3055, but that's long out of print, in favor of Tech Readout 3055 Upgrade. Sheets for the Marauder IIC and its variants can be found in the Unabridged Tech Readout 3085 Project Phoenix Record Sheets.