3. How can a monster harm a character in a new and unusual way?
Damage/Hit Point Loss... nope, that's not new, unusual or interesting.
Loss of Levels... slightly more interesting than losing hit points, as a general weaking effect, but not very new.
Applying Penalties or Negative Traits... this concept allows the fiction to have a direct effect on the mechanisms of play, and completes the loop by having the mechanisms of play inform the ongoing fiction/narrative, and it's generally how I've done games for a while, but it's been around in games I've seen for more than two decades.
Attribute Reduction... while it can be interesting, it's an idea that has been around for a few years.
Instead I'm thinking that we should look at effects like those from the Rust Monster...where metal weapons tend to do more damage in a game, but hitting a rust monster with a metal weapon rusts or corrodes it into uselessness.
Or maybe we can look at the effects like the Weeping Angels in Doctor Who. They drain temporal energy from victims and transmit them into the past where they will live out their days and often die before they are even born.
Technically, all of the effects that "injure" a character could be interpreted as ways to deprotagonise them, reduce their ability to impact the ongoing storyline. A reduction of hit points makes combat riskier, negative traits make tasks associated with them less likely to succeed (or more likely to backfire). A character has to wait out the penalties, or heal the effects until they can reassume their intended role as "heroes/protagonists/central-characters".
What's something unusual that might do this?
In the current real-world political climate, a monster that changes a male hero's gender, a white hero's skin tone, or a cis-character's sexual preferences might be severely impacting on them... but you'd need a mature group who could handle such things properly if you were going to include such a creature in your game.
Maybe a creature that pushes an opponent slightly out of phase with reality. Being out of phase might mean that the afflicted character looks a bit translucent and fuzzy, out of focus... the effect of this is that delicate work is impossible, and most actions are slightly more difficult. Every time a character is hit by such an attack, they are pushed further out of phase, where they might have a higher likelihood of encountering nightmarish creatures who exist on the edges of reality. Naturally, a mortal soul seeks to exist in sync with reality, so these attacks might heal once every hour or so... but during those hours, life is a nightmare for those afflicted.
Mechanics of play... every successful hit has a 50/50 chance of inflicting a "Desynchronised" token, every hour that a character has "Desynchronised" tokens, roll a d20. If the character's d20 roll beats the number of tokens, they avoid encountering one of the phase monsters (who may inflict more tokens). If the character rolls more than twice the number of tokens (or rolls a 20 if they have 10 or more tokens) they lose a token. If a character ever earns more than 20 tokens, they are permanently desynchronised, never to be seen again.