I answered your question in your private support ticket but since the information could be helpful to anyone else I will share it in this public thread as well.
Test Studio maps only the default required fields in the QC configuration. However some of the custom fields you have added in the configuration as required could not be mapped since they are beyond the default settings and absolutely expected an error occurs. Please change your QC configuration to require only the default fields. This should allow you syncing between both tools.
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