Follow the Rules > Tactics section. In short, during PO you cannot TIE but CT has the same effect on enthusiasm as Regular Season Normal, and Normal has the same effect as a Regular Season TIE.
It's not wise to CT at 5, because you will find yourself at 2 or 3 in your next game. Most people would tell you to absolutely avoid it, but I say: if you really need that win, go for it. Just bear in mind that it will take 4 or 5 games to get back to 5, unless you TIE them. I once CT'ed an important game with 5 enthusiasm, I won it and managed to win the following games even with a very low enth., thus gaining home court advantage in the PO so it can definitely help although it's very risky.
Not sure what you mean with the last question, of course it's wiser to TIE when playing home where you have an advantage, but it's impossible to say if you'll win anyway (especially if your opponent CT's in the same game: this can be a very tricky mind game, I'd suggest to check your opponents' attitude in their previous games before making a decision).