how bitcoin mining works [duplicate]

The way I understand mining is that you hash the previous block hash with the new transaction files and a variable to get certain amount of zero in the hash.

You have chain A-B-C-D- , you create a new block, E, with its header (with variable called nonce and a reference to D's header hash) and body (the new transactions). You change the nonce in E's header and then hash the header. This hash should have certain amount of zeros.

So the stronger your hash power is the faster you find the new block hash.

True, but searching the correct hash means guessing the nonce from entire range of nonces, and everybody guesses their own variable. So the fastest computer will only have highest number of guesses. This doesn't mean someone else with only a few guesses won't guess it first. Like in a lottery, the guy who buys 1000 tickets is not sure to win comparing to the guy who bought 2 tickets, he just has better odds.

and how do they get rewarded ?

Only the one who guessed the hash is rewarded.

because the websites that offers hashing powers shows your balance to be continuously increasing and not as expected to increase step by step with each hash found.

If this site is a mining pool it gives rewards by some strategy, rather than giving the reward to the one who finds the hash at the moment when he finds the hash.

When mining in a pool, you're rewarded proportionally by the hash rate you provide versus the total hash rate of the entire pool, or some variation on the theme.

The probability of finding a valid block hash is such that one block will be found in around 10 minutes regardless of the total hash power of the entire network. This is the "difficulty" number at work. Therefore, unless you control 51% or more of total network hash power, you are no more likely than anyone else to find the solution for the next block.