Q1: Since there is no central authority controlling Bitcoin, then, who is actually giving out Bitcoins for miners for securing the network?
When the miner solve the block (every 10 min on average), he is rewarded by 50 btc (25 btc now, and it will decrease over time). The blockchain contains all the transactions since the first block, and they know exactly which address has btc, and how much. So, you have a full historic. The bitcoins are directly credited to the miner's address