Based on your follow-up comments, this all sounds like normal RPM ranges. 2,000 RPMs right at startup is normal, just as long as it goes back down after a few seconds or so. (it may stay higher for longer when it’s ''really'' cold out).
As for shifting into Drive, the RPMs will slightly go down because the engine connects to the transmission, and the resistance of the transmission fluid takes energy from the engine and lowers the idle speed slightly. Vice versa, when shifting into Park, the RPMs will go up temporarily because that resistance is no longer there. Your car’s computer will notice this and bring the idle RPMs back down to the normal 800-900 RPMs.
That’s all a bit oversimplified, but I hope it makes sense. There doesn’t appear to be anything wrong based off the info you gave.