1) Bitcoins are generated by computing a hash of a predetermined difficulty. By putting forth the "work" to find the necessary hash and adding it along with the list of associated transactions to the blockchain, the "miner" maintains the security of the global bitcoin register (blockchain). In exchange for completing this work, according the the constraints of the protocol as implemented, all the miners and client programs agree that the miner can add a transaction for a predetermined amount of bitcoin (currently 50) to the blockchain assigned to themselves. Per the protocol, the difficulty of the hash is modified regularly such that the estimated average time for the total hashing power of the entire bitcoin network to find a satisfactory hash is approximately 10 minutes. As computing power increases, and the number of miners on the network increases, the hash difficulty is adjusted accordingly. A successful hash will only be accepted into the network if the majority of the nodes agree that it meets the protocol requirements. There may be 'breakthroughs' which might drastically increase computing power, but this will only cause an increase to the difficulty of the target hash. New blocks will still average about 1 every 10 minutes.
2) They have the force of the free market requiring them to be accepted at the current market rate for anyone who has an interest in using them.
2b) Yes, they can currently be broken down to 8 decimal places (0.00000001 BTC is often referred to as a "Satoshi"). With enough agreement in the bitcoin community, the software implementing the protocol could be modified to break them up even more. Due to a computer's ease of working with numbers, bitcoin can essentially be broken into however small a piece the economy requires. If 52" plasma TV ($600 USD?) is 1 BTC, then a pack of gum may be 0.002 BTC ($1.20 USD) or 200,000 Satoshi.
3) Deflation will cause big problems for the continued activity of an economy that is built around an expectation of inflation. Bitcoin is built around an expectation of deflation. I'm not sure if an intentionally deflationary economy has been built from the ground up with participants aware that the currency is intended to be deflationary. I suppose given the rarity of gold, and the ever increasing population, the gold standard economy may have been a bit deflationary. It will certainly be interesting to see how it all plays out. I expect that within 8 years the growth rate of new currency in the bitcoin system will have slowed enough for us to get a pretty good idea how exactly the economy will react to this. Between now and then, anyone making predictions in either direction is likely to be doing more guessing than actual predicting.
4) Rate of mining production is approximately 50 BTC every 10 minutes. This will be cut in half to 25 BTC every 10 minutes in a few more months (maybe sometime in December). Then approximately every 4 years the rate will be cut in half again. The equation is such that the total bitcoin ever produced will be approximately 21 million.
As for the number of bit coins currently in the economy, see the stats here:http://blockchain.info/stats