Yes, they do. In fact, one of the trendiest colors right now is called Greige. Search for it in the box above to see examples under "Ideabooks." It should solve your carpet issue.

I think grey can compliment beige well.

That is a very good question. Yes, you can definitely use gray and beige as your main furniture fabrics. It is sometimes better to use more neutrals for your main pieces and then use throw pillows, artwork, or wall paint as your pops of color. This way if you ever want to change your accent color in a year or so, you don't have to go out and purchase all new furniture.

They absolutely do, I doing it right now in my living room!