you should get a temporary certificate right after the auction and tax deed in 60 days after the auction.
you are the new owner right after the auction as well. you can start an eviction immediately as needed.
the tax deed provides a clear deed as far as other liens are concerned. however the county does warrant the deed. you may need to wait for 1 year in case anybody challenge of the validity of the tax deed auction.
once the grace period is over, you can get title insurance. once you get title insurance, you don't need to worry about the title any more.