Skynet didn't know about Sarah, Kyle and John when it sent back Arnie backwards into the first movie, which created a future where Skynet still won, but after that, Skynet knew enough to target John when he was Ten and not miss by an inch which failed so insanely that Judgment day never happened, then some one edited the last 5 minutes out of the movie and the it seems as if Skynet did again after all still win till 2030 something because they had so much information on the resitance that they could target 20 + of his lieutenants + the wife + they had Johns DNA on file(Which should have thrown up some flags if they had Kyles DNA on file from when he was ni a work camp?)... Did you see the T-800 in the first movie cross check the DNA of all the Sarah Connor's he terminated? But even after the events of the third movie Skynet still won till the fourth decade of this century and it would seem that they were sending more t-800's and John was sending more Kyle Reese the metal bastard which is an odd redundancy (which we never viewed as multiple kyles and T-800's fought over the right to see who would fuck sarah (Literally and figuratively respectively. )since a timeline doesn't change till after a traveler enters a timeline destroying their own future since it becomes impossible (Predestination is a gimps game.)for them to have been sent into the past if they were already there making the changes they thought would redirect time with and...
Each iteration gives (each) Skynet more clues about the shape of the past.
Skynet has survived more than once by using alternate backups to restore its systems after a main facility is destroyed. Following T1 a backup processor was activated in Los Angeles. Following that it was restored to the original CRS facility for Terminator 3. They do actually destroy it in the T3 storyline (at least in the novel) as the last copy is supposedly destroyed.
As for multiple combatants in the past: I've long assumed that Skynet has sent multiple teams back in time to accomplish its goals. If they killed, for example, John's top lieutenant in one storyline how would they have ever known he'd existed in the first place? In the novel of T2 (T800 and T1000 were sent back the same date) they knew John Connor existed because they were in the temporal chamber when the changes caught up with them so they knew to send someone back to protect Connor.