Yes-laws do vary state to state--- most states are "at-will" work states--you can quit or be fired without notice--this is usually the case unless you are a contracted employee.
As far as unemployment--try it... Everyone I know who has applied for it gets it--although i know my company fights it everytime~~they are jerks about it. Usually you can get unemployment unless you were fired for gross misconduct.
And as far as getting another job after getting fired-- ask them, since they are willing give you a reference, if they agree to consider your termination (as far as other employers are concerned) a resignation. BUT-- make sure that is only with other employers-- you cannot get unemployment for resigning. Make sure to be very clear with them.
Good luck-- I can honestly say (and I never admit this) I was fired from my old job--my old boss was a dick!!! We had personality issues--he didn't have one

--seriously-- he wrote me a bad review, i asked -in writing-for a follow up in 6 weeks, he told me okay-at 6 weeks he told me that things were great and he would get that written up in my review--the next day told me let's go to hr to write up the follow up on my review--he fired me!!! He told me is was poor performance, but asked me to stay 6 more weeks--- the vp of hr knew we had issues--i asked why would you want someone who did shitty work to stay for 6 more weeks--hr manager agreed something was not right-- told me i could go home--he would get me a check for 3 months pay plus sick and vaca days. also agreed to pay for a headhunter, and agreed that my employment record would reflect i resigned and they not fight unemployment. also agreed to still pay for reimbursement for my mba, that i was 1 month from finishing.
I am so sorry this happened to you---talk with the company--see what they are willing to compensate you with.
-wendi