Stuck at 9-3, is this when I should reincarnate?

Yep~ Reincarnation is the key point in this game! When you reincarnate, your money, upgrades, and stages reset, but you get reincarnation points which are permanent. Also, stages you've already cleared get a x2 speed boost. Skin effects stack, and I bought the very last one first, then bought others as I could afford them.

Is the skin a fish pet? You need to level up 3 of them and reincarnate to go faster. I got bored around level 40...

Yep yep, you have to keep reincarnating this.