Opening night tickets are usually made available for purchase closer to the night in questions. I've seen many opening night performances end up of TDF or TKTS. Yes, they are usually the less desirable seats--mezzanine or balcony, depending on the theater.
In my experience of attending opening nights: They tend to start later, because people mingle before the show. Aside from that, it basically goes off like any other performance--except that, because the audience is stacked with friends and family, people involved with the show, and other arts professionals, there tends to be more entrance applause, etc. Usually the entire production team (director, writer, etc) come out for bows at the end.
"You travel alone because other people are only there to remind you how much that hook hurts that we all bit down on. Wait for that one day we can bite free and get back out there in space where we belong, sail back over water, over skies, into space, the hook finally out of our mouths and we wander back out there in space spawning to other planets never to return hurrah to earth and we'll look back and can't even see these lives here anymore. Only the taste of blood to remind us we ever existed. The earth is small. We're gone. We're dead. We're safe."
-John Guare, Landscape of the Body