No, not really. The "3nm" in the "3nm process" is not a measure of anything in particular, and even if it is a measure, the measure may or may not be in the neighborhood of 3nm.

Several years ago, fabs started naming each next-gen process with a smaller number of nanometers, even if the process size didn't change. It's just marketing now.

Process and architecture are mostly independent.

Node process is determined by the physical manufacturing. Architecture is determined by the design templated on during manufacturing. You could make an arm core on an intel process (which I think even happens in some of their testing phases). So yes.

No. At these nodes it's all marketing.