This is what Common Ground calls the conference’s legacy resource, and it is the argument for filling a presentation page in properly. The page outlives the week by a very long way.

A conference issues three documents at three different moments, all from the event’s card under My events. The two letters download from Download letters and certificates; the certificate appears on your own proposal or presentation listing.
The certificate is automatic but not instant. An administrator verifies participation first, so if you need it for a deadline, allow for that rather than expecting it the moment the conference closes.

Membership is a year of the network’s journals and books, read or downloaded from the Bookstore, plus the community’s own feed — and a cheaper way back to the conference after this one.
The conference was the event; the network is the thing it belongs to. Presenting put you inside it, and that does not lapse when the dates do.

Presenting is not the end of the work. There are two routes on from it.

Permanently. The digital media does not come down when the conference ends, and neither do the presentation pages.
On your proposal or presentation listing, on the event’s card under My events. It arrives automatically once an administrator has verified that you took part, so it is not there the moment the conference closes.
Two routes: the conference’s own proceedings, and the research network’s journals, which you can submit to separately.
Yes. Discussion boards never close, and the presenter is notified twice over however long afterwards it is.
No — an audience pass does not carry membership. Presenting does, whatever the presentation type.
Yes. A peer connection is platform-wide and has nothing to do with the conference; it stays until one of you ends it.
Yes, on its presentation page — which is also still the place to ask the presenter about it.