As of August 24, 2024, the past fourteen months have been the hottest on record according to NOAA.
Each question will resolve based on if NOAA determines the specific month to have been the hottest month on record for that month.
September 2024 was the second hottest September on record.
https://www.ncei.noaa.gov/access/monitoring/monthly-report/global/202409
August 2024 was the hottest August on record.
https://www.noaa.gov/news/earth-had-its-hottest-august-in-175-year-record
NASA is different record though I believe they use many of the same temperature records.
Shows August at +1.30C compared to last years record of 1.19C.
These temperature records are normally very similar but August 2024 may be an exception.
https://data.giss.nasa.gov/gistemp/tabledata_v4/GLB.Ts+dSST.txt
Note this isn't the data that matters.