Affected sensors when boosting another car

No, as long as you are jump starting properly there should be no damage to your car. It's possible that your battery could be drained a bit doing the jump-start, and a low battery could cause starting issues. A way to remedy this would be to drive your car for a bit after doing the jumpstart to make sure the battery is fully charged, or rev the engine for a few minutes.

Of course it's very possible this issue has nothing to do with jump starting at all. If you try what I suggest above and you still have problems starting then it's definitely not related.

Ok, let's see if I can help! First, let me explain: I own a car repair shop here in Brazil and happened to had a similar problem once with my wife's Kia Cadenza, and sometimes I had to turn the key (not pressing buttons, but the same) like 2, 3, sometimes 10 times until the car starts. I tried to diagnose via OBD2, but no log was recorded whatsoever. So, after a little hacking, I noticed that the starter motor relay was ticking, but the starter motor didn't run. Then I tested the relay on the bench and I noticed that even when turned on, it remained open (circuit). Plus, I use a wire to try to directly start the car and the car started. Then I bought a new relay and the car never had this trouble again. It's a very cheap part, may worth a try.