Well, the lenders won't tell you what their mimimum allowable credit score it (I tried to ask when I was turned down by a few) they won't give that info up.
I was eventually able to get qualified through the Sallie Mae Law Loans at prime +5.5% (which is their highest rate) but at least I was approved, without a cosigner, when I was turned down by conventional banks for their law loans)
I don't know my specific credit score, but its not great.
As far as raising it, my guess is a minimum of 60-90 days... it takes them that long to update crap