Car Dying

I drive an early 1994 mazda protege 2.0L DOHC. This car has been randomly shutting off while I am driving, frequently when I am letting my foot off the gas pedal. Sometime it will start right up again and sometimes it takes a lot of tries to get it going and when it starts hard like that there is usually a large amount of smoke in the exhaust.

It was fine most of the winter until a month ago when I could not get it to start again without push starting it. I paid a mechanic $50 to tell me I had a bad battery and nothing else. I replaced the battery and everything ran fine until today. I was driving down the road and it shut off again. I popped the clutch and it started up again but now I’m very concerned. It had been worse usually in the warmer weather. I just did a tune up. New fuel filter, air filter, cap and rotor, plugs and wires, PCV valve. I’ve cleaned the entire air intake system and just replaced all the belts as well. Any suggestions?