Rule 44.3, Scoring Penalty, applies at an offshore event.

If a boat touches several marks of the course, does she need to take a Scoring Penalty for each incident?

Yes. The Scoring Penalty replaces the One-Turn and the Two-Turns Penalties (see rule 44.1). Therefore, a boat may take a Scoring Penalty when she may have broken rule 31, and this applies to each individual incident, similarly to the One-Turn Penalty.

If a boat touches a finishing mark, is she required to cross the finishing line from the course side for a second time after she took a Scoring Penalty for touching it?

No. As the Scoring Penalty replaces the One-Turn and the Two-Turns Penalty, rule 44.2 does not apply. Therefore exception (a) in the definition ‘Finish’ is not applicable. The boat finished when she initially crossed the finishing line from the course side.