If I do a run with no DLC weapons or charms and the highest grade. Could I submit it to the any% no DLC, any% DLC, highest grade no DLC and highest grade DLC. All in a single run?

You can submit a highest grade run to any% as well, but if you did not use DLC items you cannot submit it to DLC.

So you have to use at least one charm or weapon from the DLC to submit to DLC. Got it