Could the air become unsafe after exposure to radiation?

Radioactive particles (dust) in air are problematic. The gas in air does not become radioactive (at least in a dangerous way) from exposure to radiation.

If the surface of mars is exposed to radiation capable of making particles become radioactive, does that mean the surface is already radioactive? Or would this only happen to airborne dust particles, not to sand particles on the ground?

The dust itself would have to be something highly radioactive like uranium. Radiated silica isn't going to get into you and cause real issues.

Couldn't irradiated silica dust get into your lungs though?

If you're breathing silica dust you're going to get silicosis anyway, so there's not much point worrying about it.

Maybe the living area buildings inside the tent can have a vestible / "dustlock" for keeping the dust outside, and outside those it just becomes standard to wear a dust mask.

Dust is one thing but it’s the fines that really get you.

If you’re putting all of your eggs in the “shielded other structures” - why have the other structure in the first place? It’s not as if you can live outside those “other structures” if you’ll just die of radiation poisoning.

Or, to put it another way, any structure capable of shielding against cosmic radiation should be capable of also holding air (we’ve gotten really good at that).

> any structure capable of shielding against cosmic radiation should be capable

A thick roof without walls should protect you from cosmic radiations (some distance from the edges), yet wouldn't be airtight....

A large rubble pile would do the same.

You need much larger structures for growing food than for living. Food can handle the radiation.