One of the few merits of Exalted's mechanics is that you can usually improvise exactly what you want with only a little thought. Look at those race rules you seem to want. You just laid out an extended contested (Dexterity+<relevant ability>) roll with a varied difficulty for each person. That is already contained in the rules! No complicated subsystem needed, just a basic outline and some stunts. As long as you set the required threshold at a decent level (I hate the way the rules default to only 3 successes in a game system where your dice pools are in the 20-30 range), your players won't care that they aren't using the Athletics Combat Subsystem 2.5.

Gateway is actually mentioned in at least one place as an extended opposed (Intelligence + War) roll. IIRC there are even a few modifiers, but the game is intentionally left vague so you can stunt your plays to fit the situation. If you want to run a trivia challenge or a test of riddles, then an opposed extented (Int + Lore) roll sounds like the way to go.

As for your mental combat idea, I'll be blunt and tell you that I think it sucks. When it comes to knowing things, you either know them or you don't. Opposed Intelligence+Lore rolls won't make you smarter or him dumber, nor will they make him more likely to accept your superior intellect. Social rolls are how you convince people of things.

However, I will agree that Exalted does need true Mass Social Combat rules. I'm not talking about the stupid "convince everyone who is present at a scene of something" Mass Social Combat that we currently have. I'm talking about the sociopolitical and economic interactions between companies, political factions, and even entire cities that is supposed to be represented by the Mandate of Heaven rules but that fail miserably at their job.