My car has trouble starting. I have to try it a lot before starting. Cuts off 2

What is your question?

Every time I try and start my car I have to try and crank it repeatedly before it finally starts. New battery. Car also kinda cuts off while driving. It sometimes seems like I took my foot off the gas pedal then kicks right back in or on in some cases. Just bought car didn't do on test drive not sure what the problem is.