(2) the right way to do this is to train a probability estimator on your scores, that is, put +/- labels on some of your documents, then apply logistic regression.
http://en.wikipedia.org/wiki/Logistic_regression
A lot of machine learning people think this is harder than it is and worry more about regularization, overfitting and such, but in the case of turning a score into a probability estimator you are (a) fitting a small number of variables and (b) if you have a lot of data and make a histogram you will ALWAYS get a logistic curve for any reasonable score, I think it has something to do with the central limit theorem.
This seems to be one of the best kept secrets in machine learning. I used to be the bagman who supplied data to people at the Cornell CS department and we ran into a problem where there was an inbalance in the positive and negative set and in that case the 0 threshold for the SVM is not in the right place because it gets the wrong idea about the prior distribution and T Joachims told us to do the logistic regression trick.
Also if you read the papers about IBM Watson they tried just about everything to fit probability estimators and wound up concluding that logistic regression "just works" almost all the time.