Should I dilute DNA with water or elution buffer?
I would generally recommend using the elution buffer (which is typically Tris-EDTA buffer) or TE-Buffer, as the pH and the conditions stabilize the DNA for a longer time, which is especially interesting when you want to store your DNA.

It also dependent on your downstream application - when they recommend diluting the sample in water (or another buffer) I would follow this advice. In my experience TE buffer is perfect for all molecularbiology applications (cloning, digestion, amplification, PCR, etc.). The EDTA will of course complex bivalent cations, but since the concentration in the buffer is only 1mM and the DNA solution is usually diluted further in PCR or digests, this plays no role in real life applications.