With the Trueskill system in place, is the rating more significant than the rank (as in chess)? Does it matter if you are an 1800 standard player, or a top 35 rank player? I think the former, but I'd like people's opinions.

If the rating is more significant, couldn't we display real time rating on the profile more prominently, letting it act as an ELO of sorts (on certain competitive settings)?

Well, it is hard to answer your first question. First, TrueSkill promotes activity, so as long as you play on your level, your rating will go up due to reduced variation (at least in theory). Besides that we don't even know if there will be an inflation effect in the future so I personally would give more importance to rank.

About the 2nd part, all the other ladders display both rank, rating, best rating and best rank. Now since Fizzer did not yet implement it there are 2 possible reasons behind it, either he does not want it at all or, what is more probable, he waits untill the ladder is more active and templates are tweaked (goodbye diplo and LD :) ). That is probably the reason why there are no trophies or achievements for real-time ladder.

Despite Fizzer earlier saying he would later implement it, I didn't think he would as I don't really consider the other ladders comparable to the RT one. If anything, I expect a trophy for the RT ladder to be temporary; given to only the current number 1; the current best strategic player in the game (assuming the less strategic templates are replaced with better ones).