If you paid for repairs in 2017 you would claim those expenses on your 2017 return if the rental was still active.
If a third party reimbursed you for the repairs in 2018, enter that as income on your 2018 return.
When the rental is first put into service the basis is determined. You can't adjust that. If you add value to the property with adding an "Improvement" such as a new roof, pool, or room addition, that improvement is added as an asset of the rental and also depreciated.
For example if the property was purchased for 200,000 of which 20,000 is the value of the land, 180,000 will be the value of the building and depreciated. If 5 years later the Fair Market Value of the property is 250,000 and you add a new roof for 12,000, the basis of the rental building is still 180,000 and the roof is now a new asset with a basis of 12,000. The roof will now also be depreciated.
The value can't be increased because of inflation because you will pay capital gains on the rental when you sell it. The gain is based on what you originally paid and the improvements you made. You will also "recapture' the depreciation you have taken on the building (and assets). Exclusion from gains of real property is only when the house is a primary residence and meet certain requirements. Even in this situation, any depreciation claimed (or could have been claimed) is "paid back".
