Wires only pick up current when they’re moving through a magnetic field. Just sitting in one is fine. Although the internal compass isn’t going to work great.
Also people significantly overestimate the amount of current a normal (something you’re gonna encounter in day-to-day life) magnetic field can induce in a wire. There’s a good reason motors are packed with so many windings, you either need an incredibly large magnetic field, or a crap ton of wire, to get an interesting amount of current.
Current also picks up force as it moves in a magnetic field, but it's not like the electrons are going to fall off.
Magnetic fields can saturate ferrites and affect coils, but the slight deviations in few components should be nothing the closed loop circuitry won't handle. You'd need a stronger/closer magnet for that.
Solid state circuits usually have tiny sensitivity to static magnetic fields as opposed to EM waves, which they need to handle gracefully.
The reason for magnetic field strength falling off as 1/r^3 is interesting: the biot-savart law says that magnetic field falls off as 1/r^2 from a magnetic source, but in reality sources tend to be better approximated by magnetic dipoles than magnetic monopoles. A "north pole" is always accompanied by a "south pole", and at distance there are "interaction effects" such that a part of the field strength is "canceled out".
Also people significantly overestimate the amount of current a normal (something you’re gonna encounter in day-to-day life) magnetic field can induce in a wire. There’s a good reason motors are packed with so many windings, you either need an incredibly large magnetic field, or a crap ton of wire, to get an interesting amount of current.