12 people are sick with measles: 9 of them have been VACCINATED, and 3 - UNVACCINATED (!!!),
2 of them have rejected from vaccination, 1 kid had age limiattion.
(...)
The main is that kids who should have been protected from the disease get sick 3 times oftener than kids with natural immunity who weren't hurted by chemical injections!

Your math is correct if and only if exactly half of the population in the republic is vaccinated against the measles. Reductio-ad-absurdum, consider if there were only three people in the republic who were not vaccinated, and all three of them got the measles - the claim that "the vaccinated are three times more likely to catch measles" would obviously be wrong.

If 2/3 of the population is vaccinated, one could be tempted to conclude that the vaccine neither helps not promotes the measles. I believe that the real percentage in Bashkortostan is closer to 95%, though I'm of course guessing here.

Also, the numbers aren't statistically significant. The only conclusion one can draw from it is that the vaccine isn't 100% effective.

As for the whopping cough example, you may have a point - I don't believe there is any conspiracy going on, but a doctor would probably be a bit too quick to write a diagnosis, not even considering the possibility that someone that is vaccinated against whopping cough would have the whopping cough.

I do believe the situation today with the health-care heavily relying on a profit-driven "big pharma"-industry is quite sub-optimal, and of course there are risks with vaccines - but in general, I do believe in vaccines. Thanks to vaccination, we've eradicated Kopper, we've almost managed to eradicate Polio, and the Measles has become a rare disease.

The success of the vaccines may be their downfall - yes, since the measles are such a rare disease, the risks of taking the measles vaccine probably outweighs the small risk of getting the measles. This logic is true as long as everybody else takes the vaccine. For the society as such it would be ideal if 100% of the population got vaccinated, this could cause an eradication just like with the Kopper.