1) I guess so, the blockchain contains the bitcoin transactions.

2) In order to add a block to the blockchain, you need to mix the block's fingerprint with a random value and shake, hoping for the mix to get a special and very recognisable appearance. If it doesn't work, you have to try a new random number (the block's fingerprint of course stays the same). When you've found a good number (which takes a lot of tries and luck) you raise a flag and say "hey, found it", and you can add your block to the chain. Then you're rewarded with some amount of bitcoins that are created from nothing (hence mined). I don't have clear how this reward is granted, whether it's already written in the block you're trying to add or in a new one, and in which form.