Whether Fourier transform formula be considered as Convolution or Correlation?
Correlation and convolution are basically the same operations. You can express the cross-correlation of two functions $f(t)$ and $g(t)$ by a convolution:

$$R_{fg}(\tau)=f(\tau)\star g^*(-\tau)$$

where $\star$ denotes convolution, and $*$ denotes complex conjugation.

If you evaluate the cross-correlation at $\tau=0$ you get the inner product of $f(t)$ and $g(t)$, and that's exactly what the Fourier transform is: it is the projection of $f(t)$ on the complex exponential $e^{j\omega t}$.

So, to answer your questions:


It is actually an inner product. Due to the equivalence of convolution and correlation, it can be seen as both, evaluated at $\tau=0$.
As already mentioned, the meaning of these terms is an inner product.