Slippers/barefeet are not allowed by all powerlifting organizations. As for training, it is usually benificial to pull from a slightly higher position than you would in a meet, at least every other workout (eg off a 100 lb plate). I personally wear converse All-Stars (Chuck Taylors); they give good support and have a low sole on them.
As for your other question, that is very debatable. Many powerlifters wear a bench shirt in a meet and the belt is partially used to keep it in place. Wearing a belt can help take some strain off your lower back, if you are an archer (eg butt and shoulders on the bench, but back arched). Some people also use it, to get a better valsalva compression for their lift.
Hope this helps some.
pax,
GS