Hi Ilya,
Now that you have
linked your Google Analytics and AdWords accounts, you can then retrieve Analytics related fields via the AdWords API, and they are listed in this
section for your reference. As for the conversions that you mentioned, if they are conversions tracked from Analytics, then I'm afraid that this is currently not supported via the AdWords API.
However, in order to make sure that we are on the same page, could you send to me the screenshot of the AdWords UI view wherein you are viewing the said conversions? You may reply to me via the Reply privately to author option.
Thanks and regards,
Peter
AdWords API Team