"Does the showerhead I ordered swivel, or do I need an additional part for it to do so?"
It is rare for a showerhead not to have a swivel feature unless its position adjustment is in the shower arm or it is a "flat" model that is meant to be installed parallel to the floor. With the exception of those mentioned, some industrial models and most handshowers, standard-style showerheads generally come with a built-in swivel feature.

"Why can't I buy a showerhead that puts out more water?"
It is now a federal law that all showerheads sold in the United States must be low-flow.