No, you cannot use the carpet change and repairs as improvements because you removed them from service as rental to personal use in the same year you did the work. There is no deduction for this, however it should be added to your cost basis of the home for a future sale.
You should indicate the property was used 100% of the time for rental in 2024, however you must also select that it was converted to personal use and enter the date it was converted. Do not enter personal use and rental use days. This will allow the correct depreciation for the rental period. It also answers the question appropriately. The key is that you must adjust any other expenses that would apply to both the rental and personal use period such as mortgage interest, real estate taxes, insurance, utilities, etc.
Yes, as indicated you need to prorate the amounts that would belong to both personal use and rental use. Enter the correct amount in the rental and also, in the personal itemized deductions enter the difference that are for the personal use days. Do not duplicate amounts in either section.
In your example you can divide by days as an easy formula, which would be appropriate for taxes, property tax. However it's quite likely you paid more mortgage interest early in the year. Check your statements at the mortgage lender to see the actual amount paid until September 15th, enter that on your rental, then use only the balance on your personal itemized deductions.
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