Are pools share rewards equivalent to the power/hash rate input of a mining machine I would like to know if I enter a pool and I input a given amount of Hash rate, is my share reward equivalent to my Hash rate input
Yes, it is. This is done by the pool having a much lower difficulty than the network does. If your block meets the pool's difficulty, you earn a share (but the block isn't really used); if it also meets the network's difficulty, then it is released to the network. Finding shares is random, and the payout scheme can mean that you earn more or less coins for a share, but over a little time it averages out so that you are paid proportionally to the hash rate that you bring.

As a simple example, a pool that uses a proportional split scheme would split the mining reward to the miners in the pool based on how many shares they earned in the course of mining that block. (This scheme is not good, because it allows pool hoppers to earn more at the expense of other miners, so other schemes like PPLNS are more common; but that's more complicated so I'll leave out the details.)