No... The key phrase there was "quit my job."
No, you must be available to work and actively seeking work to qualify for unemployment.
In Kansas you can collect unemployment if you "Quit to enter training approved under the Federal Trade Act of 1974" so there is a possability
No x 2: You cannot get unemployment benefits if you quit your job, and you cannot get unemployment benefits while going to school full time (regardless of why you aren't working).