How to pronounce The /r/ as in RED /r/ in American English

There are actually two correct ways to make it, as long as the tip of your tongue never touches the roof of your mouth. You can curl the tip of your tongue backward, or you can bunch the middle of your tongue up toward the back of your mouth. In either shape, the sides of your tongue must press against the insides of your upper back teeth to anchor the sound. Both techniques produce the exact same R, and Americans are split about 50/50 on which one they use naturally.

You're letting the tip of your tongue touch the roof of your mouth. In Spanish, Italian, and Russian, the R is made by tapping or trilling the tongue against the alveolar ridge just behind the teeth. In American English, that same tap turns into a fast /d/, like the flap T in water. The fix: pull your tongue further back, keep the tip free, and let the sides of your tongue carry the work by bracing against your upper back teeth.

Yes. Bringing the corners of your lips in slightly changes a lot. Tongue placement creates the core of the sound, but the lip rounding is what gives the American /r/ its dark, thick quality. It shouldn't be a tight pucker like a /w/. If you say red and it sounds like wed, you've rounded too much. Just flare the lips a little forward and the /r/ has somewhere to anchor.