I have a payment arrangement for 2020 property tax on the home I own. The payments are to be complete by June 2021. Do I still claim the 2020 home taxes on this return?

No, do not claim a deduction for property taxes that you haven't paid yet. Deduct property tax payments in the year that you make them.

Individuals such as yourself are cash-basis taxpayers; you only report income you have actually received and can only deduct expenses that you have actually paid.