I collected four pots and things, is there more? What else should I do to get the alchemy lab out of ruins?

Not just pots.

chalkboard

Where or how do I get the chalkboard?

There are 5 things in total:
red and yellow pots, potion bowl, vase, and spear

Ah, the spear is what I don't have.

Same here; where is the spear?

It should appear when you've restored the lab.

Lying around like the pots. The locations of pots and the "spear" tool change from game to game. So yours would not probably be in the same place as mine, or Herbella's, and so on.

That makes sense, thanks; what does it look like, though?