Does a characters' regular physical attacks also have their innate color attached? I.e., is a Black Innate character more susceptible to the physical attacks of a White Innate character and vice-versa?
I don't think so...I think this only occurs when you have a Sigul thing equipped and have an Element used on you...
Actually I'm pretty sure they are. Just look at the difference on the S.S. Invincible part where EVERYTHING is black. Serge does awesome dmg even with normal melee. What I usually do (well, just did, as I'm playing through CC for the first time now) is use 5-sta with serge attacking, then TurnWhite on Glenn, then send him in. If it's two monsters, the fight is done, and if it's three, it can sometimes STILL be done, as I use a white element with Glenn too.
But the attacks are ALWAYS their innate color. Just look at the "swoosh" effect when they swing their weapon. Serge's is always white. Glenn's is ALWAYS green, Leena's is blue, etc. You may not always notice it, but the "effect" is ALWAYS their innate UNLESS a "Turn(whatever)" is used on them. As in my example, Glenn's usual green "swoosh" turned white.
Wasn't sure about your first point though. I always tend to load-up people with their innate color, but it definitely isn't in the manual that your innate affects their casting power (I looked last night for this very thing). Your vulnerabilities, and summons, and your melee attack, and I figured PROBABLY your element casting as well, but are you SURE?