What particles are made with two quarks, and what restrictions are there on the two quarks in it? I'm pretty sure it's mesons, but I don't know the restrictions.

What particles are made with three quarks and what restrictions is there on the three quarks? Again, I think it's baryons, but I don't know the restrictions.

You are correct. As for the restrictions go, baryons consist of three quarks, and mesons consist of a quark and an antiquark.