f''(2) cannot equal 3 and 0 for the same value of x. That's a contradiction. As a result, both of your sentences "For example, f''(x) = 3, and f''(x) = 0 when x = 2." and "What does 2 = 3 mean?" are meaningless.

The second derivative being zero does not imply that there is a point of inflection. If you know you have a point of inflection, then the second derivative is zero. So the implication only works one way. My favorite mnemonic device for remembering the second derivative test is the following:

I can answer you better if you refine your questions.