There is nothing inherit bitcoin to force banks to keep a reserve, but neither is there with physical cash. There's no reason a government couldn't impose the same restrictions on a bitcoin bank operating in it's country. Of course, bitcoin makes it easier to run a bank like this, but it also provides a way for anyone to check how much BTC they actually have in reserve.
Of course, this isn't the only way to generate 'money' like that. Admittedly my understanding of this is only basic, but I thought most governments had given up trying to control the money supply anyway? That they couldn't control it because there was always new ways of creating cash substitutes?
For your second question, each bitcoin transaction has a transaction fee associated with it (which can be zero). It is up to each individual miner to decide which transactions to include in the block, and currently they give a higher priority to ones with a higher transaction fee. As to who gets this fee? The miner who solves the block gets all of the transaction fees as well as the new coins. My understanding is that even now, free transactions are on the way out. The current standard fee is 0.01 BTC for reference. The idea is that as time goes on, most of the reward will switch to transactions fees over new coins.
As for bots, it's not true to assume that there is no opportunity cost for mining. As they mine, it becomes more likely that they will be detected. Every 10 minutes or so, you need to start working on the latest block (or else everyone else will ignore your chain). Then there is the increased resource usage (most malware tries to stay under the radar so it doesn't get noticed and removed). They could mine slowly of course, but this makes it easier for the legitimate network to outhash them.
If we look here: https://en.bitcoin.it/wiki/Mining_hardware_comparison an E7300 can do 7.8 Mhash/s. That's running fult tilt, and it would be very noticable if your PC was doing that 24/7. Let's say that you can run it at 10%, and the computer is on for half the day, so 5% (keep in mind laptops are outselling desktops, so I don't think this is so unreasonable). Now we're down to 400 khash/s. The total current network hashing power is roughly 2 Thash/s now, and increasing rapidly. You'd need 5,000,000 bots to equal that, and even then the reward would only reduce by half. Now CPU mining is very inefficient compared to GPU mining, but high performance GPUs are rare and most of your bots won't have them. It would certainly reduce that figure though. The point I'm trying to make, is that it's not as easy to do as you might think at first.