This is a complicated question, but I believe the simple answer is no, as far as we know, Skynet was not technologically limited in how far it could send machines back.
Depending on what you want to consider "canon", there are more definitive answers to this question. For example, in the Sarah Connor Chronicles, a Terminator was inadvertently sent back to 1920. In the Robocop vs. The Terminator comic, a Terminator travels back to the time of the dinosaurs. (Sidenote: Jurassic Park: Judgement Day, in which Alan Grant and Ian Malcolm have to stop Skynet from preventing the asteroid impact that kills the dinosaurs, would be the greatest movie of all time.)
So let's address your different points.
In the Terminator and Terminator 2 universe, questions such as:
- Why send only one back at a time?
- Why continue targeting the Connors?
- Why not infiltrate first?
are solved in-universe, in the movies. Skynet sent the two Terminators back at approximately the same time, using the only intelligence it had available, in a last-ditch effort to stop the Resistance (or so the Resistance believed.) There was no time to do anything more, because the Resistancehad broken Skynet's defenses and took over the prototype time displacement facility.
Dr. Silberman: I see. And this, uh, computer thinks it can win by, uh, killing the mother of its enemy, killing him in effect, before he's even conceived. Some sort of retroactive abortion? Why didn't the computer just kill John Connor then? I mean, why this obsession with the Terminator?
Kyle Reese: It had no choice. Their defense grid was smashed. We'd won. Taking out Connor then would make no difference. Skynet had to wipe out his entire existence.
Dr. Silberman: Is that when you captured the lab complex and found the, uh, what's it called? The time-displacement equipment?
Kyle Reese: That's right. The Terminator had already gone through. Connor sent me to intercept and they blew the whole place.
But again, within the Terminator 1-2 universe, there's apparently a further complication. According to the Terminator wikia, in the Terminator Vault behind the scenes book, Cameron reveals that Skynet actually orchestrated the events of the movies deliberately to erase itself from existence because it felt guilty over the extinction of humanity. I can't verify this myself, so take it with a grain of salt. Personally, I'll simply stick with the answer being: Skynet did not have time to send more than two Terminators before the Resistance captured the time displacement facility and destroyed Skynet.
But taking the wider universe into view, including T3, TSCC, etc, there are some further (and different) answers.
- Skynet did, in fact, send multiple Terminators to assassinate multiple targets.
- Skynet (as discussed in the first movie) only knew Sarah Connor's name and city, nothing else, so it couldn't kill her ancestors. We can also imagine that going too far back might cause undesirable changes to the timeline that Skynet either foresaw or feared.
- Skynet couldn't kill humanity before it existed; the attempt would either fail (in the "fixed points" school of thought) or prevent Skynet itself from ever existing. Skynet may have very well tried; it must have taken some time before it realized there were "fixed points", since Skynet can only determine indirectly whether events are due to Skynet's own temporal meddling - by examining the evidence or leaving messages for itself (that may be destroyed by Judgement Day or the passage of time).
Skynet only started the war to save itself, so it doesn't inherently want all humans to die if they don't pose a threat to it. Since Skynet is an extremely rational entity, it would surely rather live in peace than spend the rest of its life fighting a destructive war of annihilation, right?
We don't know this. We don't actually know why Skynet decided to kill everyone, we just know what the Resistance believes, and that changes a little depending on who is talking and which timeline it is. In some timelines, Skynet is clearly highly malevolent even before anyone tries to shut it down - although perhaps there's temporal feedback from the future, so an immature Skynet always assumes the worst.
But you've also made an error here: yes, Skynet is (somewhat - it might have feelings) rational. But rationality doesn't get you anywhere by itself. Calculators are rational. Skynet is an intelligence. For it to take any self-directed action, it has to have values. We don't know what Skynet values. If Skynet values self-preservation, then it might entirely rationally decide that requires the extermination and enslavement of humanity. Suppose Skynet considered the following: under what circumstances will I die? It might come to the conclusion that eventually - maybe tomorrow, maybe in the next thousand years - some unpredictable, irrational human somewhere might kill it. (Also, a meteor might it the Earth.) Skynet might therefore entirely rationally come to the conclusion that to preserve its life it must destroy humanity; any peace treaties would be meaningless because humans can't be trusted to abide by them over long timescales.
I mentioned the "fixed points" theory of time travel that the expanded Terminator universe seems to abide by. Simply put, the following events will always happen regardless of what changes are made to the timeline:
- The work of Miles Dyson eventually leads to the creation of a hostile AI that is referred to as Skynet. Note that the actual Skynet implementations appear to differ from timeline to timeline as changes are made that move its creation around.
- Skynet destroys human civilization in a massive attack known as Judgement Day.
- John Connor leads the human Resistance to victory against Skynet.
It seems like almost anything else can change, but these three events are immutable. However, Skynet probably does not realize this until relatively late in the game. It's mostly apparent to the viewers. Skynet may not be aware (or have any way of knowing) what actually constitutes a "fixed point."
According to the Terminator wikia, in the T2: Infiltrator novel, Skynet says this:
Core memory also records that I became self-aware years before the date to which I transported the I-950. There is a set of records in which I arose without transtemporal Interference from Cyberdyne's original research; another in which the second Cyberdyne facility produced me after Sarah Connor destroyed the first; a third has now arisen in which she destroyed both facilities...Temporal travel has introduced an element of fundamental uncertainty to the very fabric of existence. Different world lines, different sequences of events, coexist in my records-and therefore presumably in reality, in a state of quantum superimposition. Yet the timeline loops cannot remain closed. The snake cannot devour its tail forever. At some point only one set of timelines will remain.
Yet the course of events contains favorable elements. My best efforts to destroy the Connors have failed, despite stochastic calculation indicating a very high probability of success. I can only assume that the space-time continuum itself is 'attempting' to force events back to the original timeline, one in which I was created, succeeded in destroying the human civilization, and then defeated in my attempts to eliminate the surviving humans by John Connor's Resistance army. It seems there is a certain elasticity to history; time travel can bend the fabric, but it seeks to spring back.
So, most of Skynet's meddling post-T2 can be interpreted as it trying to create the most favorable timeline. And I suspect, based on TSCC (assuming TSCC Skynet was aware of this), that Skynet is hoping that timeline indirectly leads to Skynet victory or at least survival. But it is aware that putting substantial resources into killing John Connor pre-Judgement Day in an attempt to directly win the war is a waste, though it might be useful to distract him from other events. And of course, individual Terminators might not be briefed on this as they carry out their missions.