There's not really one right answer about board scores for peds genetics.
I'm one of the 7 current peds-genetics residents at CHOP (2 fifth years, a fourth year, two second years and 2 first years). I would say on average our board scores are the same as our classmates and that's what you'll find across the country (the average board score will vary according to the peds program attached.)
I'm happy to share my scores for reference: I got a 234 on step 1, 236 step 2, 236 step 3
Research is a major component of being a pediatrics-genetics candidate. About 90% of the combined residents in the country have PhDs, but it's not strictly necessary.
There are a handful of IMGs accepted to combined programs, and again, that will depend more on the peds program attached.
I either interviewed at, or know people who interviewed at every program in the country and I'm happy to answer any specific questions you have (we're a small community) Send me a PM