When you pronounce /r/, generally, the tip of you tongue does not touch anything but the sides of the back area of your tongue may touch or slightly touch the side of your back teeth, right?

Yes, the sides of the tongue may touch the UPPER back teeth.

It helps if the tip of the tongue points up without touching anything.

The lower lip should not move. In the New York accent, the lower lip

is pushed out; do NOT do this.
Got it! Thanks, Anon.