Re: Mining new coins
It becomes harder to mine the more mining power the network has. It does not depend on the number of mined coins.
The block reward halves every 210,000 blocks, which is about four years. This doesn't make mining more difficult in itself but it absolutely does make it more difficult to earn the same number of bitcoins, even if the network hashrate doesn't change. It's also means that if you know how many coins have been mined, you can easily determine what the current reward is. The reward began at 50 and has halved twice so far and the next halving will likely occur in less than three years.
The network adjusts the difficulty to keep an average rate of one block in 30 minutes.
One block is mined every 10 minutes on average. Because the mining is a bunch of random busywork, you might have two blocks mined within a few seconds of each other, or no new blocks for an hour or more. The difficulty is adjusted every 2016 blocks, which is two weeks at the average block discovery rate, but is generally shorter than that in periods of mining power growth. If the network falls in a heap at some point, you have to wait until the end of the current 2016 block period to adjust it, which could take some time...