How will a magnet damage my 4s?

A magnet cannot damage your iPhone - the screen works by capacitance. The only thing it could perhaps affect is the compass, though I'm not certain it would. Gluing anything directly to your iPhone, though, will probably void the warranty. I presume you intend to attach the magnet to the case, not the iPhone, yes?

Why not just buy one the plethora of car/truck mounts, though? There are many available, including some that can hold an iPhone in a case, and they're not terribly expensive. Many allow you to adjust the placement and the angle of the iPhone for easy access. A much better solution than a magnet, IMO.

Regards.

I don't think magnets affect modern screens. Yes, they did affect old CRT screens.

I would be concerned about a strong magnet in close proximity affecting the compass. It would almost certainly affect its immediate operation and might even affect it permananely (I have permanently messed up a standard compass by holding it too close to a strong magnet).

No. Locations services works via the GPS, not the compass. It could affect turn-by-turn directions, though.

As varjak paw says.

Location Services tells you where you are by radio signal GPS from satellites. The devce also contains a standard magnetic compass which provides screen orientation. So if you were using this in your car it would provide your correct location on a map but might tell you you were heading west instead of north.

Moving more into the theoretical aspects here, it is possible that a strong magnet may have unexpected effects. Frankly moving an electrical conductor (such as all the wires in your device) in the presence of a magnetic field generates an electric current (and your phone is full of things sensitive to electic currents). While I am sure they design those things to work under normal conditions, I don't know if they expect you to slap a strong magnet right up against the thing and drive around with it jiggling there. I have an idea! You let us know. 😉