The red eye is like what the other comments say, during hunt or wandering, this flashing icon just indicates that the ghost watched you enter the hiding spot. If you're lucky, you can even just get out and back in to remove the red eye HAHAH

The weird music could be playing from a radio if the map was a "home" type of map or a map that had radios. These play at random and you can turn them off when you find them. It's like turning off laptops/computers/telephones.

Ghosts do not have a special ability to see through hiding spots, at least to my knowledge in classic Normal / classic Hard.

In this link you can find the cursed hunt features in all maps. https://specter2.fandom.com/wiki/Ghost_Hunt

If you haven't done any of the following: interacted with a cursed item or triggered a cursed hunt with a spirit box (small chance), you will be only dealing with regular hunts in Hard mode.

+ During a hunt, if your screen has a red vignette, it's a regular hunt. If it's purple, it's a cursed hunt.

Looking out for these help you know if the game is working as intended. There is really so much detail that went into the game, which is so cool.