3-HP Mode appears only in Lunar Shadow.
I may be mistaken on this, but Bad Heart Mode appears only in Pteriforever's Solar Shadow 2.
So what does Bad Heart Mode actually do? Also, are there any other modes in the game or is that it?
Bad Heart Mode… you'll have to ask Pteri. I'm unfamiliar with it since my source is the first wiki Kim made for the Lunar Shadow Project.
On second thought, I don't care. The modes in Lunar Shadow are more important anyway.
On a (semi-related) side note, for internal links to this wiki, you can use [[articlename]]; so something like [[Life Capsule]] or [[Entrance (LS)|Entrance]] would become Life Capsule or Entrance.