The timeline is so messed up in Terminator that it's not going to work perfectly either way, but the first point is explainable.
The movie is set after the "Judgement Day" date as they knew it in the timeline of T1/T2, so I take it as the next iteration of the timeline, with the John Connor who sent back THIS Terminator being the one who went through the events of T2, whereas the Terminator that got sent back in T2 is the result of the timeline that only factors in T1, ie. likely a timeline where Judgement Day was not stopped in 1997, but T1 happened. At some point, there must have been an original timeline where Kyle Reese was not John Connor's father, but that's another story.
So the Terminator of T3 was programmed by the John Connor who went through the events of T2, and programmed this one with some of that knowledge, rather than the blank slate of T2.
It's been a while since I've seen T3, but point 2 seems fairly inexcusable, and seems like just a throwaway callback at the expense of logic for a joke. This is a John Connor who has spent his life off the grid because of what happened in T2, so the fact that Terminators are churned out on assembly lines should be second nature to him.
That said, I still quite like Terminator 3, and don't think it's the abomination that people make it out to be. It certainly wasn't a necessary film though.
I've only watched Salvation once at the cinema, but it didn't live up to the future war that was shown in the first two movies. Again, I didn't think it was quite as bad as people make it out to be though, but it could have been so much more, and also had a lot of problems.