For solid core NTRs, the exhaust hydrogen being irradiated isnt the worry, it's that the pieces of the core may be eroded and present in the exhaust.

Also no shadow shields for crew?

Sort of? The article doesn't state whether it's going to be open cycle or closed cycle.

But I'm assuming it's going to be a closed cycle solid core nuclear thermal rocket so presumably, no irradiation plume in the exhaust.

Part of the wall, part of the crew, part of the wall, part of the crew