Good questions but might I'd like to make a couple of suggestions:
Q: What are the shortcomings of the "batting average" statistic?
Might I suggest that this kind of question doesn't quite belong because it can be interpreted to position a value judgement on the stat?
Instead, do you think it might be a good idea to ask something like:
"What are the primary short hand statistics used to guage offensive proficiency and contribution?"
"What statistics tend to be the most valid predictors of offensive success?"
I guess that I'd rather not see a list of "what traditional stats suck and why" I know that's not truly what you're saying with the BA question but folks might be a bit put off if a traditional stat like BA is assumed to have shortcomings right off the bat even if those shortcomings exist.
Also, might I suggest that "SABR" and "sabrmetrics" are made into different topics altogether? Not crucial, IMO but some folks might unknowingly connect the wrong dots.