Only in Hadrons. Leptons also have charge and they aren’t made of quarks.
From a circuit perspective that makes kinda sense, but from the abstract "bit" perspective, the "switching bit" is a mechanism that operates on bits which in the end are also data. In other words there is only one type of bit: the data bit, and the switching comes on top of it.
Not really. What usually flows (in metals) are electrons. Quarks stay where they are. And when we prefer to think about flow of positive charges, the positive charge in question is a hole left by a missing electron. Physically real positive charges (ions) can flow in electrolytes though.
When it comes to electrons and positive charges, their material existence is equally non-physical. Actually, none of them might be "flowing", as the concept of flowing applies only to physical things that occupy some spatial volume and spatial location.