I'm just wondering if pots are working as intended? You always have two "free" pots right? I planted seeds in them, then used 3 extra pots for other people. My two syls grew first, but the pots didn't "unlock" again? Do I have to wait to the rest are harvested until the two "normals" pop up again?

Yep, you got it.

Basically you'll always have two pots, even if you would have used up all of yours, but if you have more than that, they won't show up.