Does this seem like a reasonable and favorable argument worth appealing my denial of unemployment claim?

I don't think you are going to be able to overcome the fact that they had written you up for tardiness and you continued to be tardy.

Am I entitled to a stipend?

If you do not meet the requirements for the stipend, they are not likely going to be required to pay you for it, unfortunately.

I don't believe there are laws that would bar them from hiring you, but they may choose not to based on your criminal background in this situation.

An I start a class action lawsuit against my school?

You may very well be able to bring a claim individually or collectively to address the fact that you are not receiving the education and...

It feels unfair but do I have a case?

If you believe your termination was motivated by some discriminatory animus (i.e. due to your race, national origin, gender, religion, etc.) then...

Hey can o give a 1 month notice to leave my job in manhattan ?

There is no legal requirement that you give a certain amount of notice to leave a job, absent some contract that says otherwise. It would be wise...

Will a petty larceny charge from 2015 effect my chances of employment if I've been crime free since then?

The law prohibits discrimination against people based on their criminal background with some limited exceptions. If your background check...

Terminate the current contract for a breach in the previous contract?

You may not be able to terminate a present contract based on the breach of a prior one, but it really may depend on the facts - you may be able to...

Unfortunately, yes. As an at-will employee, you can be fired in this situation, as unreasonable as it sounds.

Regarding discrimination?

It depends on the claim you are bringing, but generally, you can start a legal action by filing a claim in state or federal court.