No is the answer to your first question. The improvements made in the year of the sale are not an expense although they are listed as such on the sale of the asset. This must be part of the sale and not the rental income or loss. The gain on the sale will apply capital gain favored treatment and the expenses used to reduce net rental income is handled differently on the tax return. Do not enter it as repairs on the rental.
Allocation of selling price/selling expenses can be done in any reasonable method such as the current basis of assets (cost less depreciation) and total cost of land to arrive at the appropriate amount for each. Likewise you could use a fair market value (FMV) of each asset to arrive at the appropriate percentage. There are various examples in IRS Publication 544. The 2022 version has not been released, however there has been little, if any, change for 2022.
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