For this answer, I'm going to assume that the term "hanging sqaure" refers to a sqaure that is udefended, or underdefended (weak.) This is in comparison with how a piece can be hanging, left undefended, or underdefended, which means that there are more attackers then defenders. While the term "hanging sqaure" seems to have little use, I am going to use it for the context of their answer.
For question number one, the square e8 underdefended (attacked twice, defended once against White's mating threat, which make it a "hanging square." If White takes it it, with 1. Rxe8, than 1... Rxe8 2. Qxe8# follows. This a tatic called "destroying the defender (or something)." In a sense, it is a "hanging square tatic," as with how a piece is overwhelmed and won, the e8 sqaure is overburdened, and White won it.
As to quetion number two, if a piece is deflected from preventing a threat by the use of another threat, it is indeed called deflection. Your example of the Black king being deflected from the protection of the f8 square leaves it a "hanging square," as it is now underdefended, allowing for a mate in two.
I suspect that there is some relation between deflection and "hanging square tatics."
Feel free to enlighten me about any flaws in the towels section below.