How would I go about securing the bottom plate to cement?
I always use a Ramshot and use a Pressure treated bottom plate and use either cill gasket or tarpaper between the plate and concrete.
What would be the best way to make sure that the top and bottom plates are parallel?
A plumb ball on a string is the best way to do this.
Would it be best to toenail the studs to the top and bottom plates or build the frame on the floor then raise it and nail it?
Toenail (this is called stick framing) 2 on each side and 1 on each end.