State tax filing

Thank you very much for your response! Two follow up questions: 

(1) Should I split the year according to the event of when my physical office location has been officially move to UT (i.e., 10 months NY, following 2 months UT) when filing the NY tax?

(2) 2022 and on, with my employer not withholding any NY tax (and my physical office location in UT), will I be still liable for any employment-related NY taxes?