do i really need this air pump to keep the car running without any problems?

 

That is too ambiguous, we don't know your situation. However, if the car is completely stock you are keeping the catalytic converter(s) you should not remove the air pump.

By the way a simple search would give you what you needed to know...

 

ok ill be more specific. i have a 91 rx7. the only thing i have exhaust-wise is the downpipe. its a stock 13b. air box is missing. little random tubes missing. nothing huge.

 

turbo or NA? If tuebo then you only need it for emissions and if you have a cat. If its an NA then the same applies and they actuate your aux ports. you can remove it on an NA but you will need to activate your ports another way. there are many ways try a search if you are NA and interested