What you're experiencing is something everyone has likely gone through as a first-time driver. I put off getting a license until I absolutely had to 'cause of school/work.
I'm still not an expert and myself having gotten into an accident just last year, some would argue I'm not allowed to give advice but I'll give what I have.
My two cents is to get as much practice in until it starts to stick. If you have to sit in your car and practice changing between park/drive and turning on the low beams/wipers, then that still counts.
Unfortunately, this is one of those things where you'll be getting the most useful experience from actually being out there in the open. If your car is relatively modern, it should have sensors onboard to tell you about things when they go bad (e.g. tire pressure). While there's always the chance the sensors aren't entirely accurate, if your car is new or your state requires you to get your car inspected, I think you could be reasonably be assured they're working right for most things. Of course, you can always buy a tire pressure gauge and do it yourself (I have to do this a lot more in the winter here where I live).
I don't know if they have something similar to AAA where you live but if you don't, you might want to invest in a spare tire and add that in somewhere if your car is able to host it somewhere.
I don't have the know-how for how to take advantage for everything that may come with a car, but aside from what I've mentioned, I think all that's left is the usual common sense stuff that I think everyone here would follow anyway...
Congrats on your new ride!