The way student counsel elections tend to play out is not encouraging to your case.

Having considered this further, I would no longer endorse that statement. Rather, I would expect a net positive effect relative to other types of voter.

Also the problem with most of your proposed tests is that in practice they're likely to degenerate into the test writer or administrator attempting to determine how they'd vote.

While this is a problem - and one that, I suspect, rests on trying to control future government's decisions - I'm going to go through the different ideas there, just for fun.

Not allowed to vote until they decide they want to.

Obviously, does not apply.

Not allowed to vote until their parents say so.

Almost certainly applies, but then, if you trust democracy anyway...

Not allowed to vote unless they convince a panel of experts, judges, or random people off the street.

Applies, barring certain safeguards, or the "random people" option if you like democracy and juries.

Not allowed to vote until they take a simple course on how to vote.

Technically applies, but we already have schools, so...

Not allowed to vote until a certain age (significantly lower than 18.)

Probably doesn't apply ... I guess someone who gets disproportionately old or young votes might try to change the age limit, for that reason.

Not allowed to vote unless passed by a qualified professional (Doctor? Psychiatrist?)

Depends on how much you trust doctors.

Not allowed to vote until they pass an exam (Politics? General knowledge? IQ? English?)

Since this was the original and "default" proposal, obviously, this applies. Although it might be hard to sneak into an English exam.