IRA rollover

I am trying to reduce my retirement income for 2022 by $745.  I can't contribute to an IRA because I am not working and I was told that was a requirement to make contributions to affect last years taxes.  I read that the IRS allows rollover or put money distributed back into an IRA within 60 days of it being dispersed.  

 

1.  Can I do this?

2.  If I do this will it lower my AGI for 2022?

3.  Do I return the entire month distribution? Gross or net? or can it be a partial return?

 

My state has a cap of $100,000 where you don't pay income tax. Over that all pension, SS and annuity income is taxable.