Could Mars's magnetic field be restarted by its own moon? I've done some research (and I am definitely no scientist) but I am looking for answers. I know that Mars has two moons, one of which is on a orbit that could end in it hitting the red planet. Could this lead to the restarting of Mars's magnetic field, blocking deadly solar radiation, allowing liquid water to form and stay, and creating weather--and ultimately, a habitable planet apart from Earth on which we could start our first ever colony?
Short answer: No
Simply hitting a planet with a big rock does not create a magnetic field. Earth has a magnetic field because it has a molten core which spins. Mars may or may not have a partially molten core, but even if it's partially molten it's not molten enough.
In order to have a magnetic field on mars you'd have to melt the entire core somehow, and to do that from the outside you'd have to turn the whole planet molten again. That's a lot of small rocks or a few big ones. The trouble with that method is you'd then have to wait the thousands or million years for the outside to solidify enough to be habitable again. We are barely able to move a single small space rock at the moment, and that's only theoretical as it hasn't been tested in practice.
So, is it theoretically possible to give Mars a molten enough core to have a magnetic field? Yes, if you have massive resources, incredible technology, and are willing to wait thousands of generations.