What are the Halachos of Tznius regarding pajamas at night? Do all the Halachos apply, like the neckline?
All of the Halochos of Tznius apply even in the house, as indicated in Siman 2 of the Shulchan Aruch, that all the parts of the body which one usually covers must be covered at home.
One must be Tznius at home especially if there are Sefarim or Mezuzahs in a transparent case in the house.
If a hidden part of the body is exposed, it is Halachically problematic for a man to make a Brocho.
The Rebbe often mentioned the Brochos that can be received by paying attention to Tznius even at home.
עיין שו”ע אדה”ז אור”ח מהדו”ב ס”ב. שו”ע יור”ד ס’ רפ”ו סא-ג ונו”כ שם. שו”ע אדה”ז ס’ מ’ ס”ד-ה. שו”ע אדה”ז סי׳ ע”ה ס”א.