Can I cook in my (very) heavy copper unlined candy pot ?

You can cook pretty much what you would like, but avoid acidic ingredients at all costs. Acid will leach copper into the food, and that is toxic. Low doses will just make you ill, but copper toxicity is dangerous for your liver and health. The pots are great for jam and jelly, and safe due to the relatively short cooking times they will produce for that. Obviously, it's a candy pot, so most candy making will be perfectly safe and very enjoyable with it. Otherwise, I'd seriously consider having it tinned professionally. That way you don't have to be concerned.

Yes, with caution. Polenta is traditionally cooked in unlined copper pots. You should avoid using it to cook or serve acidic dishes (such as tomato sauces).