I have four legs and eat grass I am noisy when I am angry and stubborn otherwise I may be called stupid and unwise All of you have me

Clearly married but I'm a known wanderer. Some might remember an iconic old image of me trying a weird diet to boost my longevity. It's truly a coincidence that many now associate me with being gassy.

I do not lie, nor do I stink! But my name implies such unfortunate link. In fact I cleanse the roots on a dome. If you knead me well, I may just foam.

Always beside my lifelong twin, together we cushion the places you've been. I sit when you do, the same as I rise. I blush when it's cold, and I clench with surprise. What am I?

If you say me out loud, I am a door. If you think of me, I bring imagery of a cute love. If you feel me, there may be butterflies in your tummy. If you remove my fourth letter, I become the animal that Bambi feels this for.