Terminator and Time Travel

So in the first Terminator movie a Terminator and a human travel from 2029 to 1984, one to protect Sarah Connor and one to kill her.  At this point Judgement Day (nuclear holocaust that wipes out most of human life) is set for August 29, 1997. Now, since Sarah lives and John is born this still is the case. Now it would get tricky if the terminator had killed Sarah.  At that point John would never be born and then wouldn't lead the resistance, but then the terminator wouldn't jump back through time, meaning Sarah would be alive and so would John.... Oh then you have the thought that Kyle (from the future) is John's dad.  He doesn't know that, John will learn of it, but still, might be why John sends Kyle back when John gets to that point in life. Also the terminator's remains are found by Cyberdyne to first make the terminator. No problems here, so we will move on.

Terminator 2.  Judgement Day is still set for 1997.  But more terminators come back from 2029.  Here is the first problem.  Only living tissue can travel back in time, so the terminators can travel since they are living tissue over a metal endoskeleton.  But the new terminator is mimetic polyalloy; which is liquid metal, which by the established laws for time travel we know can not work.   Now then, they manage to destroy Cyberdyne's research and in doing so they can stop Judgement day.  Now here is where we run into problems. Upon destruction of the research if Judgement Day had been stopped the terminators should have immediately disappeared.  Now if Judgement Day had not been stopped an only moved back, the Terminator should know immediately.  We don't find out until the next movie....

Terminator 3.  Again, terminators from the future, this time they follow the rules for time travel, things are good.  We learn that Judgement Day has only been pushed  back, now until July 25, 2004.  Sarah Connor has finally died, and John is on his own.  We learn John dies in 2032, by a Terminator and his wife sent it back to guard him.  At the end of the movie we find out that Judgement Day happens, though John and his future wife are safe in a bunker.

Sarah Connor Chronicles.  Now we go back to 1999 and a terminator comes to protect John  and Sarah and jumps them to 2007.  We have clearly left the 3 movie and changed random things. I've read some things that say this is an alternate reality or perhaps and alternate timeline.  Now with all of the time traveling anyone who has seen Back to the Future will know that many alternate timelines exist.  So we can let this go.

The big problems come from T2.  How can a liquid metal that can take the shape and appearance of things pass back in time when we have been told that only living tissue can pass through time?  Shouldn't the T-101 have mentioned, by the way you didn't stop judgement day?  And then why did it have to destroy itself, since by the fact that it still existed clearly the technology is made and it could have stuck around to protect John. 

Ain't time travel fun?