If the engine loses a fan blade, it will vibrate violently and it's probably better to lose the engine.
I don't know about the other two things you mention. Maybe it's a newer feature than my time :-/
That's the idea with a fan blade loss, they didn't want to just drop an engine in that case so the centering mechanism on the turbine has an intentionally weaker part is designed to snap off to allow the spinning turbine to recenter itself as opposed to vibrating the whole structure off and causing more damage.
The gear thing is to prevent puncturing the fuel tanks in the wings on a hard landing. It's preferable to snap off the gear, otherwise leaking fuel has a good chance of it immediately igniting.
But yes, in a full size passenger aircraft I would expect the specification for wings falling off to say "avoid"
It isn't on any aircraft I've heard of. Only the engines have "fuses" which allow an engine to rip itself off without taking the wing with it.
The wing root is the strongest part of the airplane (because that is where the maximum forces are).