I refinanced my house and closed on 12/28/20 with a different lender. I did not receive 1098 loan since my first payment was in 2021. Do I need to the report in 2020?

No,  There is no need to report the purchase of a new home.  Furthermore, there is no mortgage interest to record.  So on both issues there is no need to report anything.

You should have paid 3 days worth of interest at the closing (to the end of the month).  That is reflected on your closing statement and is deductible in 2020 even if you do not receive a 1098. That is the only item from the new mortgage that would be included on your tax return this year.