A: Yes they do. Emails sent from an event are sent as email campaigns, so every contact who receives one counts towards your Marketing Automation tier.
The Marketing Automation tier is based on Unique contacts with marketing events current month. A contact is counted once per calendar month, however many emails it receives. A contact that submits a form or visits your website during the month is counted the same way. Emails you send to a single contact, outside an email campaign, are not counted.
The same event emails also count towards the Email Marketing tier, which is based on Unique contacts emailed current month. The event itself counts towards the Events tier, which is based on Launched events current year.