@2637 Health Clearance would come from your primary care physician. BTW, they may have never been asked to give it, so you might need to coach them a little bit. That document will need to be notarized locally and then forwarded to your State's capitol to be apostilled (the notary version that carries weight overseas and certifies that a document is original*). Google the appropriate address and process for your state.
A proof of no criminal record comes from the FBI. They will do an official background check. That also needs to be apostilled.
If your English documents are not apostilled they will not be legitimate in Kazakhstan. This is because your English documents need to be translated into Russian (and/or Kazakh) and notarized. A KZ notary can not notarize a translated document unless it has been first apostilled by the foreign government. Their job would be on the line.
I am speaking about the official process. I have never heard of people being successful using bribes to get through the red tape. So, for moral and practical reasons, I would not suggest it. I have witnessed people getting through with less-than-legitimate documents, but that was a literal miracle and does not happen often.
