In order to generate bitcoin, do i need to run the miner 24h/24 or i can run it for only 12 hours/day?
I suspect that when i plug off the miner, i'm interrupting the calculation in the middle and i can't resume it when i plug it on again, it will restart from the beginning.
A miner is doing millions/billions of calculations per second (1 MHash/sec = 1,000,000 hashes per second). Bitcoin has no concept of progress or state, each hash is an independent chance to win, just like a random lottery ticket. So yes, while you will "interrupt" the calculation, what you'd interrupt is a single hash, which takes a millionth of a second or less to compute. No significant loss.