1. You can use the same size hub with a SS freewheel, but you may have to re-dish the rim (pull the rim off-center using spoke tension) and use a spacer on one side of the hub in order to get the rear cog to line up with the front. Some hubs are made for SS and are made to align properly without any spacing issues.
2. Singlespeed generally implies freewheel. If someone is talking about fixed-gear in particular, they will usually specify.