It is typical for a microphone to have a non-flat frequency response like so:
Yes, it is typical for microphones to not have a flat response curve. It is really hard to manufacture them in a really dead flat way. Even measurement microphones can look like this:
which while much better than the example you gave, is far from dead flat in the higher frequency ends.
Is it typical to flatten the response curve by weighting the signal in frequency domain to get the most accurate representation of measured sound?
That depends on the field you do your stuff in. For the most part it is all about subjective quality of sound. If you want to do real number measurements, then they do it, but they start with almost flat responses of the mic anyways.
If yes, then why don't manufacturer ever provide the response curve in numerical form?
What numerical form do you want to have? What single number represents the whole graph? Essentially none is capable of doing so. The best you get is some frequency range which says "Between 20Hz and 14kHz we are not entirely totally crap". Which is why good manufacturers provide these graphs, and when you buy mics without that graph you don't care about it anyway.