My car has been driving like a dream, mostly...

So, one thing I've noticed is sometimes the starter/flywheel will make some noise if I was running the car, stopped it, then started it like a minute later. I replaced my battery 4 months ago, and upon first start the motor spun faster than the starter could keep up. Now, there is a sharp gear sound. This sound also comes on a standing rev, when it goes anywhere above 3.5k RPM. Could this be something related to motor mounts? Trans mount? Etc...

Another thing I've noticed is on a standing launch, no throttle, off break, then on the throttle the car lurches HARD forward. Also, if I give it enough space in first it takes off hard, but not until it lurches hard. (I hope this makes sense) What could this be? Diff mount?

If video is needed, I can try and get one, but the lurching is going to be hard to do as I don't have s G-force monitor