Another (unique) starting problem on 95 Sunfire

[JJLuke]

Hey guys, thought I'd present to you my little problem with my 95 2.2L Sunfire.

A few days ago, my car started having serious problems when cranking. I haven't driven it for a day or so. The car would crank but it wouldn't turn or catch... after a few unsuccessful attempts, I cranked continuously for 30-45 seconds and it started bogging and began slowly catching.

Had a real rough (1500-2000) idle for about 30-60 seconds, white smoke came out of the tailpipe, smelled a bit like fuel (not sure though), and some smoke came out of the engine bay underneath the exhaust manifold. Following that, the car idled fine.

This morning, the car had not been running for about 10 hours garaged. Cranked it, 5 seconds and it started, rough again, then smooth.

Went to work, car was parked outside for 9 hours, a little cool, but decent weather, cranked it, took nearly 12-15 attempts at 30 seconds each before it finally turned over, rough, then fine.

Went home, started the car multiple times in good order when the engine was still warm!

Other issues (maybe related or unrelated): the coolant light comes on/off intermittently, the check engine light comes on/off intermittently when running. Also recently replaced alternator and serpentine belt.

What is wrong here? Where should I start looking? I'm real confused as to why my car fires up decently when warm but has trouble when it's cool. Never had problems previously, and the battery power and ignition seems to be all there. Not too thrilled right now with my car.