The condition ends after a long rest regardless. No you can't harm him until you pass the save or long rest but every 6 seconds you have a small chance to break out of it.

Heroism isn't prescriptive it's descriptive.

I am rolling your charmed condition but your intelligence is so low and at a disadvantage by design that it's a very small chance you will ever be free. Also you will become apathetic due to his passing.

You could search him but you cannot remove magic items outside of specific conditions. If the user is dead, or willing or if the timing is right, like at sunrise or full moon or whatever the conditions state. For example you couldn't remove a magic ring, but you can cut the finger off and take the ring. I highly recommend it.

In the process of stripping him, Cat would lose her grip.

that would be interesting. Alice searching ans stripping Nezzner of magical tools would help but I doubt charmed allows that.

[Ashley] the frightened state came from my wild magic, that's highly unlikely to happen again.

Heroism only grants immunity to the Frightened condition, right? If it broke Charmed, it could have been used to free Alice. If not I would cast it on Cat.
And while Cat is the opposite of Yulya, she feels that this is way to easy. Something bad will happen when we 'kill' Nezzner.