Can Riven jump over skillshots with her 3rd Q?

Riven's 3rd Q launches her into the air briefly, allowing her to leap over thin walls and minions.

Can Riven use her 3rd Q to leap over skillshots like Jinx's Super Mega Death Rocket, Lux's Final Spark, or Veigar's Event Horizon?

No you can't jump over a skillshot with riven, however her Q (and E) are still good tools to simply dodge enemy abilities.

In League of Legends you have to differentiate between blinks and dashes.

Blinks will cause you to be teleported from point A to B instantly whereas with a dash you will travel from point A to B really quickly.

Since every instance of Riven's Q is a dash in which she remains vulnerable (unlike Maokai W for example), she will get hit by a damaging ability if she tries to pass through it.

It's even possible to knock her out of her animation using a knockup at the right time (Thresh E, Maokai Q), causing her Q to have absolutely no effect while still going on cooldown.

Riven's Q leap is a displacement, not a blink - so she will still get snared by Event Horizon.

As for the other two, I'm not 100% certain but it doesn't make her untargetable, so the Q shouldn't allow to dodge those skillshots without moving away from the line of fire.