Starkiller
Super Freak
To answer your first point, it's really messed up, the idea of John letting one in close because of his T2 experience is fine, likely it was programmed to say or do things to suggest he could trust it and reprogram it to have his friend back, but, how would Skynet ever know about that, according to T2 and T3, the Connors live off the grid.
Maybe but he's smart enough to know that all machines look like that. Whether they say they are good or not. Let's see a machine that looks like his mom...