if you were a jedi knight and youd just built it, you would KNOW it was going to work, there'd be no need to test it!
Which is a great way to lose an arm during LS practice...

On the plus side, she then went on to become Queen of an entire empire, so I guess there is a bright side to everything!
And the crystal requirement tends to vary depending upon which source you are quoting. Thus it seems most likely to me that the main requirement is that the gem be
really,
really perfect in quality. Since perfect symmetry is generally rare, this no doubt led to all kinds of stories about where the best gems could be found. As for only a Jedi being able to create them, I doubt anyone except perhaps Kuat would have the technology to align a crystal against an energy beam down to the micron level in a clean room environment. Hence the requirement for a Jedi to be able to enter an advanced level of meditation in order to be able to align the crystal so cleanly and perfectly.
Just to muddy the waters even further, some Jedi also constructed their LS to have the activation switch *inside*, essentially restricting its use to Jedi only in a rather irritating fashion. But for non-Jedi a vibro-blade is a far more effective weapon anyway.