Are deleterious brca 2 mutation carriers much more likely to get radiation induced solid cancers (from diagnostic radiation) than non brca 2 carriers ?

I say "No": It's hard to do good work, but the study you probably saw was https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3435441/ from the BMJ; that it's unreliable due to recall bias is obvious ("Yes, I know why I got cancer, I think I remember that...."). These memory-based studies produce hugely-conflicting results. The radiation you get from routine imagine is much less than the natural background.