This is a scarf cut. It's required on round logs and is done with a chainsaw. You find the centerpoint of the end of the log, measure three inches to either side and using a level, draw two vertical lines, then repeat at other end of log.

Using a chalkline, snap the two parallels, then cut out the material wth the chainsaw.

This is a 2 inch overhang. It's essentially an aesthetic consideration. It adds nothing to the strength of the structure.

Overhangs can be as little as zero to as much as several inches, depending on the angle of the joint and gap between logs.

This is a half inch gap. This allows for installation of wiring. The gap can increase or decrease, depending on preference.

A deeper gap adds considerably to cost, of course, since it has to be covered with chinking material.