Quote Quoting gonzodude
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1) What recourse, if any, do I have to sue them? (BTW, they did hire me on a "provisional" 90 day probationary period, which I signed and agreed to be an "at-will" employee for the first 90 days)
In CA, you're an at-will employee forever, not just the first 90 days. However, no, you don't have any recourse to sue them just as they had no obligation to keep you employed.
2) Will I be eligible for UI compensation? Or did I get screwed? (I guess I should mention that I had been working full-time for my previous employer for 1 year)
You should be if the reason why you were let go was because you were too slow and they didn't feel you would catch up fast enough.

This whole thing MAJORLY sucks because the new employer put me in a huge financial bind,
No, you put you in a huge financial bind. All your financial decisions were your own. They offered you a job, they evaluated you and decided 2 days in there would be no way for you to acclimate yourself, get up to speed and meet their expectations 3 weeks from now. They're under no obligation to keep you for 3-4 weeks while work is piling up because you need to get yourself together...
not to mention my financial situation was already terrible to begin with (I have been on the brink of filing chapter 7 BK, and living paycheck-to-paycheck for the previous 12 months at my old job.

Now I don't have ANY job or ANY income ... just like that! It's hard to believe that employers are allowed to do such crappy things to unsuspecting new hires. It is just wrong!
Always expect that from now on, when you start a new job (or on any job), you should believe that every day at that company could be your last. Also, since you're now on the job search train again, don't apply for any jobs you're not qualified to do.