Just tell me how do you make it a currency of the future if most of the people (there is 7.5 billion of them on the Earth, you know?) cannot have even a single bitcoin? And, you need much more to make operations with that. Do yo permit fractional coins?

There are already fractional coins (called Satoshi) available. 1 BTC equals 100.000.000 Satoshi and therefore there are a lot more units available to split among people.

What does it mean that you "reward" the miners? You say that you call it "mining" to draw the analogy with gold mining. How do the hell you reward a successful gold miner? Do you gift him additional gold?

There are two types of rewards:
One is limited, it once started at 50 BTC per block which the miner got when he found the block. This reward is halfed every 210.000 Blocks and therefore it will be 0 one day (around 2140).
The second reward are the transaction fees. To give a transaction a higher priority you need to add fees on it. The miner which finds the block collects all of those fees as his reward.