It is Earth's atmosphere not its magnetic filed which does most of the protection against high energy particles that punch easily through our magnetic field. The magnetosphere stops a lot of particles from the sun, but if the atmosphere stops gamma rays I'm pretty sure it could handle solar radiation as well. The real importance of the magnetosphere is that it protects the atmosphere from erosion by solar radiation. Without it significant atmospheric erosion supposedly would have occured, but I'm not sure how you explain Venus.

I'm not sure what the wave of probes sinc ethe late 90's have indicated, but earlier estimates indicated Mars could have enough volatiles to produce about 2 atmospheres of pressure if warmed up. With a lower gravity thats over 4 times as much mass over your head. Chris McKay has estimated that it would wither away over millions of years without a magnetosphere, but that's a reasonable period of depreciation on investment IMO.

I'd guess from qualitative reports that Mars has less CO2 and more water than early 90's estimates would have indicated.