SV Agreement

One part singular/one part plural (despite the order) requires a plural verb. Examples below correct?

• The principal and the students are going on a field trip.
• The students and the principal are going on a field trip.

Singular verb in the sentence below because both chief operating officer and town judge refer to the same person. Sentence below correct?

The chief operating officer and town judge is Mike Smith.

When or is used, the verb agrees with the closer subject. Both correct below?

The parents or the teachers are going to be selected as chaperones.
The teacher or a parent is going to be selected as a chaperone.

Thanks.