At the energies needed to power a magnetic shield, and the precision needed to tag hipersonic debris with an electron beam, why not vaporize/deflect them with lasers instead?

Vaporising doesn’t help (the mass hasn’t changed and neither has the velocity).

Deflection by vaporising a very small part of the object can work, if you can spot it coming and hit it in time.

Assuming you can somehow detect a 1cm piece 1km away, you have approximately 10ms to accurately apply enough power to deflect it.

Would sending out an electron beam move the space station?

Of course it would! But deflecting space debris is gonna cause motion as well.