Yes, we use these words, but they have different meanings from the other words you mention.
1. Angler and fisherman are different things:
An angler is a person who catches individual fish with a rod, line and hook, usually as a hobby or pastime.
A fisherman collects large amounts of fish in a large net as a job, usually from a boat.
2. Beach umbrella and parasol have the same meaning. They both have the same traditional shape as the kind of umbrella that protects you from rain.
A sunshade is something different. Sunshades are flat, and tend to rectangular - like an awning, used to shade the front section of a bar, for example. You can get sunshades that fix onto a baby buggy, or attach to the window of your car.