Acrylic is a type of plastic. More info here:
http://www.sdplastics.com/acrylic.html
You can bond it with a few different chemicals. Some are more dangerous than others. Ether is one chemical that makes an excellent bonding agent with clear welds, but it's very dangerous to use. The fumes could knock you out, and they're explosive to boot.
Fiberglass uses either sheets of woven fibers or a loose collection of fibers that are sprayed on to a surface. It's then coated with a resin which hardens around the fibers. If you've seen concrete poured over rebar the concept is similar. Either one by themselves isn't as strong as a combination of the two.
And yup, anyone can work with acrylic or fiberglass, you just need room, ventilation and the proper tools