Just got a maz....I have a few ?'s..

Hey, if you saw my other post, i ended up buy that mazda. I have a few questions about it...first, my fuel gauge only works when im moving is that normal? If not what could cause this?second, when its cold(and a little bit when its warmed) It wants to die if you give it to much gas, to fast. What could cause this?

Thanks again for all your help..jp