Confusions regarding meaning of "kernel" in signal processing and image processing?
What is the meaning of "kernel" in context of filters?


A "kernel" is the thing you convolve by.  So for a FIR filter that's defined by the taps $k = \begin{bmatrix}a_0 &amp; a_1 &amp; a_2 &amp; \cdots\end{bmatrix}$, $k$ is the kernel.

For a 2D filtering problem, the kernel would, in general, be 2D (and you tend to see the term much more often in image processing, but I've also seen it in really highfalutin' stochastic signal processing literature).


  What is meant by "neighborhood of operation" here?


For an output pixel at position $\begin{bmatrix}x, y\end{bmatrix}$, all of the pixels in the input image that affect the output.  In general, if you have an $n \times m$ kernel, the neighborhood of operation is $n \times m$.


  Is it true even in case of FIR windows such as Hanning window,Blackman window etc? Those windows are also kernels?


Different disciplines, different terminologies.  No, because those don't define filter kernels -- the "windowing" operation is different from the "windowing" in 2D image processing.