Is Polaris really true north or just the closest visual star? Should a mount really be aligned somewhere near Polaris to be 100% accurate?

Not true celestial North, but very close. Polar alignment scopes and eyepieces will typically have a ring, often illuminated that you put Polaris on when you align. Several applications and I bet a few websites will show you where on the "clock " Polaris should be sitting for your date/time/position. (not sure position really matters)