general problems

I start my car and let it warm up (which takes like 45 minutes) and after the temp gauge says normal I try putting it into gear but it will not go into any forward gear and when I try reverse it grinds...my car idles at low 500 range..I just recently bought this car so I'm not sure what it normally idles at.
And on a side not..would you any have any thought on this problem...my fuel gauge doesn't work..after you drive it for awhile(like 20+ miles) it starts going up. But my low fuel light works properly..any clue what's wrong?

Thank you