I would like to know the proper procedure if one stays awake until midnight for Tikkun Chatzot. If so, does one need to do Netilat Yadim, and Birkat Hashachar? Can one do Tikun Chatzot at midnight (understanding that he didn’t sleep before), then go to sleep (after Kriat Shema before sleeping), and then wake up the next morning and do all the blessings as usual?

You shouldn't say any of the morning Brahcot or Netilat Yadaim, just the Tikun Chatzot. After you wake up in the morning you do them all.