I'm pretty sure you have to do something to make them fire you in order to collect. And it can't be something unethical or illegal. If you steal office supplies for example you can't collect. If you're fired for poor attendance you can.
i dont know about where you live, but where im living, the only way to get unemployment benefits after working is if you were sacked or if you had a legitimate reason for leaving, like if you were only getting 7 hours a week, or in some cases abusive managers but in alot of these cases i would go talk to someone at the government office so your sure of what the conditions and what sort of proof you need if these things are happening, tell them why you want to leave and see what they think you should do.
You get unemployment benefits if you are laid off, for example by cutbacks. If you are fired for cause, or if you quit, you will not get unemployment benefits. I can assure you that none of the complaints you had will get you unemployment benefits. You'd best be hunting a job and good luck with that, you won't have a recommendation from your last employer and that increases the dificulty of finding work.