Here's how I would do it.
The property is "in service" as of the date it was "available for rent". Period.
Since you refunded the renter the entire rental amount they paid in 2021, and you refunded it to them in 2021, I would not bother including that income in the total rental income received in 2021.
You are correct in that the insurance payout would be included in rental income.
Your cost to repair/restore the property back to a habitable condition is a property improvement. You can lump those costs all together (with exceptions) and enter them as a 2nd asset in the assets/depreciation section. Depreciation on this asset begins the day the property is available for rent, which of course has to be on or after the date the work was completed.
Furniture/appliances are depreciated over 5 years. Typically you can lump them together as a single asset entry. But that can (and most likely will) cause problems down the road. For example, if you lump all the kitchen applies together (fridge, stove, microwave, dishwasher, etc) and say 2 years later the microwave goes and you need to replace it with a new one, this can (and will) create a paperwork nightmare on the tax front.
With furniture/appliances that cost less than $2,500 you can just expense them under the safe harbor deminimus act and be done with them. But they need to be itemized on the invoice showing the cost of each item at less than $2,500 for that specific item.
Now understand that not all items under $2,500 can be expensed under safe harbor. For example, a hot water heater is one of those "grey areas" in the IRS pubs. It costs around $800. But since that becomes "a physical part of" the structure as a part of the plumbing system it gets classified as residential rental real estate and depreciated over 27.5 years.
