Is it rude to be too early for an interview?

Yes.

It's actually rude to show up excessively early for ANY sort of social engagement and, despite the business context and objectives involved, an in-person interview IS a social engagement.

Despite the professional context, you are still considered a "guest" and the employer is considered the "host". In most cultures, the host is expected to provide some sort of accomodations for the guest--if only acknowledgment of arrival and a simple waiting area considered a non-public space. By showing up excessively early, you're placing an "excess of obligation" upon the "host".

If you find that, by happenstance, you'll arrive "excessively early" for your interview. The default behavior is bide your time in some fashion that does not involve any obligation on the part of your "host" until just shortly prior to the appointed time.

Depending on the circumstances of your arrival, one can try calling ahead to ask the other party "If they would prefer, it's unexpectedly become possible to move up your meeting". I generally don't recommend this as it can greatly over-complicate previously agreed upon schedules and, if not handled delicately, can convey the impression that one or both parties don't place enough value on each other's time, attention, and prior commitments.

Of course not. Just say traffic was lighter than expected, and produce something you brought to read - one's choice of reading material could be a positive factor as long as it's not just a prop.