I think we're differing on unimportant semantics. Consider that optimal mixed strategies don't generally assign equal probability to each choice. If they were all equally good (say, as a pure strategy response) then they shouldn't have different probabilities.
I don't think so. The payoffs depend on the mix of the opponent. You can't say "the probability of sub-strategy x is higher so it must be a better strategy". If it really was a better strategy, you would pick it all the time, not in some mix.
