Hello and welcome to the forum 🙂
If the invitation table is a n:m relationship, meaning it has n:1 attributes pointing to both contact & event, you can use a n:m input field either on a form handling an event or a form handling a contact. Then you either assign contacts to an event, or events to a contact.
n:m input input fields are hidden by default (as they can be quite numerous), but you can toggle the n:m option in the form editor under "Fields" in the right side bar.
As an example, you can look at the application Organizations and at the form for editing a team - in this form, there is a n:m input for team members. You´ll find the same relationship input (but from the other side) on the form for editing a contact.
For your second question: In this scenario you could create a n:1 relationship attribute on the relation event, which also points to event (e. g. self reference). This attribute we would call something like copy contacts from events.
On the event form you could then use this new attribute to select the event you want to copy contacts from. You can then use the selected event (which to copy from) as a filter on your n:m input field for invitations (e. g. contacts n:m events). Or you could use a frontend function to resolve all contacts from the other event and copy/paste them automatically as new invitations.
There are even more approaches, like putting a button on an existing event to create a new event with existing contacts - this would also work via frontend functions.
I hope my comments are helpful for your situation 🙂
