Law is an interesting character, but I don't think he's related to Luffy's past in the slightest (nor any of the other Straw Hats/vital characters, for that matter). Understanding Law would mean to understand the symbol which his jolly roger promotes (and thus which Doflamingo is seemingly against). I feel that we will be getting an explanation of its meaning soon to come in the New World.
Regarding the whole discussion on haki, I do not see the time skip supplying any other Straw Hats with that skill besides Luffy. Granted, other members are bound to develop it over time, but they will not get control of it just yet. For that matter, I can really only see Zoro and Sanji also tapping into haki–a special treat for the monster trio. As for the complaints with Mihawk teaching Zoro, it's fitting. This won't change the rivalry the two have with each other--it only deepens their relationship. Now the final battle is also a measure between teacher and student rather than enemies.