My Own Crystal Water Fountain?

Well, the first step is going to a store that sells "everything," buy "everything," buy a water fountain and glue "everything" onto it.

Home Depot sells replacement fountain pumps. Start small, get one and go from there. Ours is the small pump that we've replaced a couple of times. The fountain is maybe 18" tall and it's just the right pump for that. Make a watertight receptacle to hold water as a base, run a tube up to the top, and make the water cascade back from there into your base. Whatever else to do is up to you.

I'm sure it's possible to do, but without knowing anything about the design you want, the size it would be, your budget and some other things on no one can say much, if anything, about how to do it or what tools you'd need.

This is difficult to answer because "Crystal Fountain" is a trademark name.

The first thing is to come up with a design and from there figure out the materials that are to be used (if they can be used). The material used for the crystals would determine what tools would be needed. Gem cutting as a jeweler does it would be beyond most peoples skill level. The use of some gems might not work because the gems are water soluble. Fake gems of glass or plastic might work. With plastic being the easiest to work with.