I like to consider off-speeds as those pitches slower than my fastball or peel drop and faster than my change-up....
Usually around 5 - 10 mph slower than my fastest pitch I would consider off speed....
It is just a term, but that is how I use it.... Hope that helps, and having off speed pitches can really help a pitcher since the batters will have a much harder time, timing them up.
U can throw different pitches with a fastball grip. Basically, depending on what is trying to be thrown, the grip is not as important than successfully achieving the spin you want for a particular pitch. So there are different grips used for different pitches, but the main objective is finding a grip that you are able to use to get the spin you want.
The spin is achieved by the angle of the release and spin off the fingers... (that is just a basic explanation)