Q: Noises happening when car is driving but stops when car stops.

So I'm not sure if these noises are related but I'll try to explain. These 2 noises started about same time. One is a low humming that sounds like it's centered up front. As soon as I release the brake, you can hear it & once I start driving, another noise, a high-pitched but almost knife-sharpening sound which is more prevalent say when I roll my window down, starts. Both stop when I stop. In addition, again not sure if related but I'm giving as much info as possible, I'm having a tire pressure monitor system issue. It doesn't always register the front right tire pressure & my light comes on. Sometimes too when I make right turns, I hear a screeching sound. My tires are still slightly new but nothing else has ever been replaced. Also a noise I hear occasionally is a more clunky one when turning or going over bumps & potholes. And sometimes my car clunks & jerks when switching from park to d/r or coming out of 1st gear. I went to a mechanic who couldn't replicate noise when lifted.

My car has 114650 miles.
My car has an automatic transmission.