How are they calculated? I got two; one for the item trade chart, which I understand, but the second was for the breeding offers chart. I never did a breeding offer, unless it's counting the one from the tutorial that everyone did (if I'm thinking of the right thing). So, how are all the weekly scores calculated?

I'm going to take a wild guess here and assume that it calculates either the amount of money made from breeding offers or the amount of times the particular animal was bred. Everyone does one breeding during the tutorial, and I think that if you buy a pet from the trades, the children from that animal from its previous owner are calculated as well.

So if you bought a pet that had offered a breeding previously - you are now listed as the owner, and that pet is being counted.