1) Should we keep logos on the 2x2 or not?
Yes
2) Is the theoretical possibility of counting parity important enough to not allow logos for 4x4x4 and 6x6x6?
No, you can put the logo on the corner , than I see no issue
3) Should we consider having different logo regulations for BLD and speedsolving?
No
4) What kinds of logos should we allow? Should they need to be a brand logo, or can we allow custom logos? Is "delegate discretion" enough to manage custom logos?
Logo's that are not raised or encraved
5) Are logos important to you for the purpose of identifying your own cubes at a competition? If so, do you feel this hurts your ability to keep track of puzzles?
YEEEES, besides this ,also for the scramblers. And in my home we have several cubers using the same brand , I will need the logo to identify my puzzle in competition, it happens to frequent that scrambles swap cubes, so with my name I can see this is not my puzzle. I do not mind to put a logo for 4x4,6x6 etc on the corner.