Both of these are physical necessities, and both militate directly against the idea of a light, comfortable radiation-proof suit or dome. They're also not something that can be solved by incremental improvements in materials science - as sensible to imagine that we're just an unknown number of iterations away from main battle tank armor with the mass and density of Styrofoam, and for precisely the same reasons.
Is anyone researching this line of thought?
Otherwise, pure mass over your head is the best defense.
https://www.nasa.gov/feature/jpl/mars-ice-deposit-holds-as-m...
If this really is just a metre down and 80% water it's got to be an attractive target - relatively easy to mine (once surface is cleared, just use heat) and a hollowed out underground structure with 1m of ice above would be an effective radiation shield:
http://space.stackexchange.com/a/1826
... and once you're there, water is water, plus water can be used to make fuel.
[0] https://www.mirion.com/introduction-to-radiation-safety/radi...
Anyway, worth pointing out that cosmic rays are little groups of neutrons (and adjoining protons). I don't know about the half life of the resulting products, though, or how often a heavy nucleus collides with another nucleus, vs simply bashing through electron bonds.