Why is only half of Mars magnetized?

To gather something that seems like a reasonable answer, you’d have to consider that while Earth’s magnetic field deflects charged particles from the solar wind, the atmosphere is also an important deflector and buffer for the absorption of other forms ionizing radiation, so even if the magnetic field deflects charged particles, like free protons, free electrons and alpha particles, there’s still the occasional burst of X-rays, neutrinos and the constant UV radiation and probably even some neutrons, which mostly gets caught by the air and distributed into the environment as heat.

So, the comparatively thin Martian atmosphere is probably a bigger deal than the magnetic field, generally speaking.

Anyway, to approximate how big a deal this all is, you’d have to consider the inverse square law, to account for how much weaker the intensity of the radiation is, given that Mars is farther from the sun than Earth is. If Earth is roughly one astronomical unit from the sun, Mars is about 1.52 units away. The inverse square law says that as the distance doubles, the signal strength is four times weaker, triple distance weakens strength by nine times. So, 1.52^2 is ~2.3104 times weaker intensity, which is partly a correlation to the disk of the sun being visibly smaller, farther away.

If the general, overall radiation is at least twice as weak, or more than 50% weaker on Mars, the strength of the Martian magnetic field being 98% weaker than on Earth, probably means it’d still need to be 49 times stronger than it is to effectively deflect an amount proportional to the solar wind which is deflected by Earth. This means that on the surface of Mars, 50 times the amount of solar wind still rains down into the thin atmosphere, and much of it is still probably scattered by the air as heat, instead of forming into a Martian Van Allen belt.

During solar storms, however, when solar radiation is emitted at higher levels, it could be a bigger deal. I think much of the particles falling onto Mars would simply ionize in the air overhead before reaching the surface (as static electrical effects, like lightning or aurora plasma), but flare-ups of sun weather could easily be a real problem, since they still are problems even here on Earth.

The fact that you can see a sky on Mars during the day means that the air overhead is doing some work scattering the inbound sunlight, even if the sky isn’t blue. The atmosphere is about 10 kilometers thick, and air pressure is weak enough to boil water at room temperature (less than 1% of standard good-weather air pressure on earth). So, the barely-there atmosphere ensures that skin cancer and penetrating rays aren’t a super big deal, because moreso than providing natural barriers itself, the Martian environment ensures people will pretty much always be in thick suits and behind thick windows and walls as a pervasive fact of life.

Only if solar wind can be modeled by a uniform field. Radiation from flares might not drop off in an inverse squared relationship, but I'm not an astrophysicist so this is just speculation.

Without knowing all that much, I know that Earth was much more massive than Mars even before Theia impacted. I assume with the extra energy available, it would be much more likely to melt all the crust. Also, our plate tectonics is still going on, so any evidence of a thin area of crust would be erased by now.