(Newbie question) Calculating the frequency spectrum

I'm quite new to this topic, with some basic knowledge however.

I need to analyse an audio signal for different characteristics.

Like the audio editor I use (an older Version of Audition, v.3) I would like to calculate the occuring frequencies.

• For every time stamp and
• the overall occurences of the frequencies of the whole audio.

If I'm not totally wrong then for calculating the frequency spectrum I have to take an interval (window) of samples. The DCT/ FFT of that returns the complex fourier coefficients (whose magnitudes are the amplitudes of the frequencies). Correct so far?

What I do not understand:

What is the frequency spectrum of a specific time stamp then? Or does it only make sense for a complete interval/ window of samples? But Audition shows a different frequency spectrum for every time stamp... Is it something like a "sliding window" there, calculated for the center sample?

Associated with the above: If it should be (the middle of a) sliding window: How to calculate spectrums for near-border timestamps (which don't have complete surroundings)?

And how to calculate the overall occurences of the frequencies of the whole audido? I can't use the sliding windows for that, as it would count frequencies multiple times (due to the overlapping) ... Is it the average of all the side-by-side (= non-sliding) windows?

Or am I totally wrong with it?

Again: I hope my questions don't hurt too much. ;-)