I am totally lost in the idea why we have to change function in time domain to frequency domain to ease with our calculations.

Let me break my question into serveral smaller ones.

1)What is the physical implication of transferring a signal to frequency domain?

(I know that in frequency domain you have the information of the gain and phase)

2)For example, in time domain a step function x(t) in piecewise, after transformation, in freq. domain it will become 1/s. It doesn't make sense to me that 1/s implies as frequency increases the gain will decrease. By looking at the time domain, it seems not to convey with such kind of information regarding the responses of other frequencies. Seriously, what does 1/s really mean? how does it relate to the time domain function?

3) Why determining the transfer function of an open loop can help to know the stability of the closed loop?

Please help.

I am totally lost.