2) From which address are the mined coins generated?
3) I heard some sort of mathematical problems should be solved. What kind of problem is that? Please ecplain this one.
4) How does the difficulty rise and drop? Who rises and drops it?
5) In the term 1 GH/s GH= gigahash... Why do we need hashes? Mining is related to bruteforcing?
1&2) There is a special transaction in each block called the "coinbase" transaction. This transaction creates new bitcoins and sends them to an address belonging to the miner (or the pool). The miner (or the pool) creates this transaction and adds it to a block before hashing it.
3) The problem that is solved is this: Given a block of transactions, find a number such that the double SHA-256 hash of a summary of the transactions along with the number results in a value that is less than the target. The target is determined by the difficulty.
4) The difficulty (and thus the target) is recomputed every 2016 blocks. The new difficulty is derived by a simple formula based on the old difficulty and the average rate at which the last 2016 blocks have been added. If the average time for a block was less than 10 minutes, then the difficulty is increased. If the average time was more than 10 minutes, then the difficulty is decreased. Each miner computes the difficulty (and the target) for themself, and since every miner uses the same values, they get the same results. Cheaters are rejected.
5) Yes. By design, the only known way to find a number that solves the problem is brute force guessing.