What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?
A kernel in the context of digital signal processing refers to the impulse response $h[n]$ of a filter. Particularly for finite length FIR kernels, filtering is carried out by the convolution operator; hence the kernel of the filter is the kernel of the convolution sum. This kernel maps an input vector $x[n]$ into an output vector $y[n]$ i.e., 
$$ y[n] = h[n] \star x[n] = \sum_{k=-\infty}^{\infty} h[k]x[n-k] ~,$$the sum truncated to a finite length for practical FIR convolutions.

As you have described, a null space of a linear mapping is the set of vectors $x$ whose image is the null vector in the range space of the mapping given by the matrix A. As the name implies it is a set of vectors and not a kernel function (sequence). The only kernel in this context is the matrix A which maps input vectors to output vectors, just as in the context of a convolution operator. $$y = A x$$