1. No, there is not a requirement to link a P2P campaign to an event, even if the campaign is intended to support the fundraising efforts tied to that event.
2. By default, when setting up an event that is linked to a P2P campaign, if you turn on Capture Attendee Info under the Attendee Info tab, one of the roles can be participant only, which would not include the link to set up a portal account.
3. If you would like to make participation in the P2P portion optional, you could also choose not to link it to the event and instead include the link to the P2P campaign in the event registration thank you message.