No - when they sell you a security, the assumption is they were long until then (holding it) and then either disposed of their entire long position or disposed part of it (in which case they continue holding it long.)

The case where they are selling you something and are SHORT the product is a special case which requires more work usually. The most egregious case was the ABACUS deal (http://www.theworkingeconomy.com/simple-explanations-of-econ...) where Goldman was actively short the product and needed a dumb customer to unload the other side (enter Fabulous Fab and his widows orphans: http://www.reuters.com/article/us-goldman-emails-idUSTRE63O2...)

No, not if they are just acting as a broker.