My question involves labor and employment law for the state of: New York

I worked for a franchise of a major chain of pizza delivery restaurants (one of the big three, not sure if I am allowed to publicly disclose of the employer), and was fired on the day of February 9, 2015. It was about -10 Degrees Fahrenheit outside and even schools were closed due to the low temperature and wind chill. I couldn't get my car to start even after banging on the starter and I was on the phone with the assistant manager and she said one person had already called in due to medical issues and that it was unacceptable if I could not make it in. I could not afford a cab for the 21 mile drive (about 30-40 minutes) and there is no public transportation. Being the only person in my household with a vehicle my only option was to ask my in laws, who informed me their vehicle wasn't working either. I informed both the assistant manager, and the owner via phone of this information. I had one write up, and it was because of an Irritable Bowel Disease episode and neither I nor the manager could find someone to cover. I admit that I was late 5 times by a few minutes, but that was months before my termination, and I was never written up or even spoken to about it. I figured they overlooked it since each time I was late by less than 5 minutes and I always called ahead to warn them.

I had a part time job for about 3.5 months with another pizza delivery place closer by but I ended up having to put my notice in as they kept adding tasks for my position but refused to increase pay. I filed for unemployment (first time in my life) and now after claiming my $0 week I was served papers saying that I was "separated under a possibly disqualifying condition" for the employer that fired me.

With that being said I have these questions:

1) In legal sense, would the situation with my car be considered something that is out of my control and therefore allowing me to qualify for unemployment?

2) Does the fact that schools were closed due to temperature help anything?

Also, another issue I had with the employer that terminated me was that I had shifts that were usually 8 to 10 hours a day, and always crossed at least one meal period. I was listed as part time but often worked 40+ and sometimes 50+ hours a week. I never got a break, and even when I had to go to the bathroom for my IBD my boss would constantly nag me from outside the door if I took longer than 10 minutes.

3) Could the fact that I never got a legal break void the fact that my boss is saying I was fired for a potentially disqualifying condition to claim unemployment?