Suits can bring material in, and do. I forget if it was the "smell of space" or the "smell of the moon" they were talking about, but I remember reading that one astronaut described the odor as like that of burnt gunpowder, and that suitborne particulates proved to be the source.

It was moon dust [1]. I don't think space itself smells of anything - surely there isn't enough atmosphere even at the ISS's orbit to smell?

[1] https://www.nasa.gov/exploration/home/30jan_smellofmoondust....

I shudder to think what the inside of those space suits must smell like...

Yeah, Mike Mullane has a lot to say in his autobiography about the earthier odors of spaceflight. Suits probably aren't all that bad by comparison with what the Shuttle cabin got like near the end of a long mission, especially if the toilet was acting up - a circumstance I gather was regrettably less rare than might be imagined by the naïve.

It's something that science fiction doesn't really explore - jokes about Trek's near-total lack of sanitary fixtures aside, even self-consciously grittier fiction like the Expanse series seems generally very disinclined to go there. I understand why, but that doesn't stop me thinking it'd be fun to see some hard-sf author really get into the weeds of why and how space makes something as elementary as the cleanly voiding of bodily waste into a surprisingly complex and difficult engineering problem.

  > I shudder to think what the inside of those space
  > suits must smell like... 

Depends.

All radiation that you care about on the space station will be electro-magnetic - i.e. gamma rays.