I have a bunch of questions regarding the Fourier transform and the frequency domain generally.

1) Firstly, the Fourier transform is used for analytical purposes as far as I know, in other words it's a mathematical operation used to find the constituting frequency components of a signal, am I right? In other words, we don't have to apply a Fourier transform to a signal for it's frequency components to take effect on whatever circuit element they are going through, but we rather use the Fourier transform to understand how it would affect these circuit elements?

2) Secondly, if the fourier transform is applied to a signal in the time domain, we want to see it's corresponding frequency components. However, would the signal in the time domain look different after the application of the fourier transform?

3) I'm assuming that there isn't a circuit used to apply the fourier transform right?

4) Last but not least, thank you very much, I know that many of these questions sound very awkward.

Also, if this post should have been posted in a different section of the forum, kindly tell me!

Best Regards.