The stage goes through as usual and is separate from the Embodiments, as are UFOs. This is the purpose of having them, it's a risk-reward thing, as you don't know which Embodiment you're getting and you're not sure how much more difficult the stage will become after they appear. The difference is that if you're going for lives the purpose is to not shoot at the Embodiment, which could be even more difficult than trying to blow up a UFO because you have to stay away from them. In the same way if you go for bombs you have to follow them, and all this has a definite impact on how the stages are played.
Yes, it'll be midboss-style. If we have spell cards and whatever in there it only obstructs vision and is a giant attention hog, which is unneeded. I don't even think portraits are needed for the same reason. The giant IDIOT EMBODIMENT APPEAR UNPRECEDENTED SERIOUS AFFAIR won't be as much of a distraction as it's at the top and it's the same thing every time, unlike portraits.