Absolutely! Food stamps are for people in your situation. It's good that you have a job and are trying to finish up school which makes it more likely that you'll get accepted faster. You may also qualify for medical and cash assistance, depending upon your income. The Public Assistance office likes to see that the situation is temporary. They may also be able to help you with your utilities and set you up with public housing, if necessary. As a single person, you probably won't get much in food stamps a month, but you should be able to afford enough to eat well if you shop at discount stores.
Yes you can and congrats for sticking it out.
Yes depends on where you live it can take a while to get food stamps especially if you do not have children, a disability or is a senior citizen. It is possible though!