I Rented My House On July 1st For More Than HUD Median Market Rents, But Now In November Of The Same Year, It Is My Primary Residence. Can I Receive The 3% Cap For The Remainder Of The Fiscal Year?

No, the cap is applied based on the status effective July 1st of that fiscal year ( our fiscal year is July 1 thru June 30).  You can change your property qualification to primary residence effective July 1st of the following year.