Quantum circuit, Fourier Transform/Decomposition?

A quantum circuit is a sequence of initialization, resets, and quantum gates - typically a quantum circuit ends in measurements. When you reuse a quantum circuit - it precedes another quantum circuit.

So in this case of QFT the implementation is over the amplitudes of a wavefunction. (Note this is different in many ways when compared to FFT that transforms a signal - input is time domain and the output is frequency domain). There are quantum circuit with no semblance of QFT - it could be energy levels when used to produce the maximized value of the objective function and so on.

Here is a good textbook to start with https://qiskit.org/textbook/ch-algorithms/defining-quantum-circuits.html