Did the listing say 'Pick up only: Free' in the search result, but 'Collection in Person' in the listing? The buyer can't make you deliver it at all, let alone for free. I would tell them that they can either pay for delivery at cost price or do a mutual cancellation.
Its your mistake to be honest. Whatever you write in your description is worthless if you havent selected the right option. Its like when people write-i will not be held responsible for items that get lost--well actually you are-means nothing. The most you can do is refund, relsit and probably be hit with a big red neg.
no they can't ask for compensation. Just be businesslike in any reply to them and don't get embroiled in arguing via email, it will get you nowhere and will just upset you.
they will prob leave a negative, but it is only a red dot on a website, so don't worry about that. You can also leave a follow up to the neg saying 'item was for local collection only as too heavy to post' or something along those lines.
If you relist, make sure you set the listing up correctly as written on the link above.
you refunded their payment in full? if so then don't worry. As a seller you get charged a paypal fee for receiving payments, but if you refund the payment in full this fee is wiped out, and the buyer receives all of their money back.