Yeah, Sumner was the second guy. I thought he phased into a wall though.
And my take on the whole SkyNet thing was that Tech-Com stormed the Cheyenne Mountain Complex and took out the SkyNet mainframe - crippling it's ability to exert tactical and strategic control. So all the machines would still be out there, but they'd basically be running in dumb mode without the Mainframe giving them proper intelligence - which would make them far easier to pick off and devoid of any unified retaliatory capacity.
The Terminator that killed Connor was probably already on-mission when SkyNet went down. But the way it's put in the film it sounds like time changed, the war lasted longer, Connor never made it to the end and his kids took up the fight when he died.
Actually the T3 movie did get a single thing right - Skynet taking over the Internet. It was designed to survive nuclear holocaust, what better way to preserve itself when pretty much unleashing it?
In the books the humans win by countinously hacking the net, and loading up viruses. Victory is achieved when infected most of the systems (as in, outpacing Skynet for a war on its mainframes.) Since J-Day happened in the 1992 they do all of this on pretty low-tech hardware (pre-Pentium era machines and no M$)
Programmers are the most sought after and precious resources in the hands of the resistance - and likewise are the prime targets for terminators.
Inflitration missions are usually a one-way ticket to hell, spent by sacrificing the team members one by one to insert the programmer into a critical facitility.
