How does a magnet affect another magnet, something made of iron or a similar metal, and moving charges?

First

Im going to talk about a magnet close to another magnet, Magnet A creates a magnetic field that Magnet B responds to that magnetic field. It either repels it, attracts it or causes it to spin to its favored position

Second

If an object is made of iron, the iron can respond to the magnet and it'll be temporary magnetizes

Third

Now the most interesting one is the moving charges. So if you have a moving charge it responds to the magnetic field and a force will be on it going in the direction using your right hand rule. Now If you have a coil and you move a magnet through it you create a current! Faradays law explains that. Thats how motors and generators work.