Terminator question 1:  when does Kate matter?

In response to Terminator part 10:  resequencing, Hesus asked:

Previously, you seemed to ignore that John and Kate's first kiss were as young teens and that if the terminator in the second film hadn't shown up and killed his foster parents and sent John into hiding (or deeper hiding?) then they would have fallen in love and married (according to the reprogrammed terminator in part 3 who said they were married in his timeline and that he had killed John before being reprogramed and sent into the past to protect Kate from the female terminator). Yes?

This is a complicated question, but a brief recap of the timelines of the series should help.

1. In the original history, nothing arrives from the future.  Sarah Conner has a child, General Brewster launches Skynet around 2004, and Sarah's child is a problem for Skynet.  Kyle Reese and Kate Brewster are irrelevant; this history ends in 2029 when Skynet sends a T-800 back to kill Sarah.
2. This T-800 is not the one in Terminator.  It kills Sarah after she gives birth.  The child still becomes Skynet's problem, which still goes online in 2004.  Kyle is born and joins the resistance; Kate is irrelevant.  Skynet sends the T-800, and the Conner child sends Kyle to save Sarah.
3. Kyle displaces the original father, and John Conner is born.  Kyle gives Sarah information, but the T-800 is destroyed in Cyberdyne's factory, giving them hardware.  SkyNet launches sooner, and the T-800 improves; Kyle has revised information.  A sawtooth snap stabilizes when Cyberdyne cannot learn more from the latest parts than from the last set.  Skynet goes live in 1997; some version of Kyle is sent to protect Sarah.  Kyle knows Sarah's child as John.  John makes out with Kate in 1997, but after that she's irrelevant.
4. That history ends when Skynet sends a T-1000 to kill young John in Terminator 2.  Everything is the same until 1997 including the party with Kate; the T-1000 never catches John, but kills Sarah and is destroyed when the bombs fall in 1997.  Kate probably dies in the attack; she is still irrelevant, Kyle is still sent, and the T-1000 departs.  John then sends the T-800 back ostensibly to protect himself, actually to protect Sarah.
5. The arrival of the T-800 saves Sarah, but she uses information from the future to alter the future.  This succeeds in postponing judgment day back to 2004, but erases the information.  John lies, programming the T-800 with the now incorrect history of Cyberdyne's involvement.  Thus she destroys Cyberdyne because if she didn't Skynet would go live in 1997, and this delays it until 2004.

   John meets Kate through his motorcycle accident when he breaks into her clinic.  No terminator arrives, but they breakfast together, and as the virus infects the Internet and cell phones and credit card systems crash, John panics and persuades Kate to take him to Mexico.  The bombs fall that day, putting them together.  They become Skynet's big problem.  Skynet sends a T-800 back to 2004 to kill Kate and others.

6. The mission of that T-800 is thwarted because John recognizes it.  It kills General Brewster before being destroyed when the bombs fall.  History stabilizes when Skynet sends the same machine on the same mission; just before doing so it kills John Conner with a T-800.  Kate captures that T-800 and reprograms it, sending it back to protect her father from the other T-800.
7. General Brewster is still killed.  Kyle is born, Kate and John escape, and history runs smoothly to the moment when Skynet was to have sent the T-800 to kill Kate.  Being now aware that another T-800 will be sent, Skynet upgrades to a T-X anti-terminator terminator, sending it on the same mission.  It encounters the T-800 which Kate sends moments later (sent in a previous timeline and so already having arrived in the revised past), which protects John and Kate as they flee to the underground shelter together.

   Terminator Salvation happens in this history, which continues through the sending of all the travelers from the future including the sending of the T-800 which established the final history.

Thus Kate needs to meet John at thirteen in 1997 after the histories created by the T-800 and Kyle Reese are formed--the third point above--but she does not need to meet him again until after the resolution of the events of Terminator 2, in the fifth point above.  That 2004 meeting at the veterinary clinic is fairly stable, since travelers from the future have not yet interfered sufficiently to change it, and under all remaining histories they survive together.