Hello Erin B
What concerns the ticket question, your itinerary is a bit tricky.
I think the best option would be the Swiss Travel Pass for 8 days. There is a youth pass for the young adults. For the first and the last day, you are fine to use full fare point-to-point tickets. For the last day, you could even use a Supersaver ticket (don’t do so for the Zurich Airport to Lucerne part, as Supersaver tickets are no longer valid if you miss the departure time due to a flight delay).
As an alternative, there is a 6 and 8 days Bernese Oberland Pass (only available from 1 April - that’s why I have asked for the travel dates). But, the price is 350, while it still does not cover Lucerne. I think you are better off buying the Swiss Travel Pass which is valid for the entire Switzerland, not only for a certain region. Of course, certain mountain excursions are not included.
Are you open for constructive criticism on your itinerary?
Living myself in Central Switzerland (Lucerne area), I suggest you to take a cruise on Lake Lucerne. The old steam boats are totally unique and I am sure, you have not had such an experience. You could combine it with a visit of Mt. Rigi, instead of Mt. Pilatus. Both mountains have a cogwheel train, yet Rigi offers by far better mountains views. Your itinerary could be Lucerne - (boat) - Vitznau - Mt. Rigi - Rigi Kaltbad - Weggis - (boat) - Lucerne.
The Mt. Pilatus cogwheel train, which is the steepest in the world, is not open in May, so you would have to go up and down by cable car.
Interlaken is a great travel hub but also a tired tourist town. Perhaps a bit less in May; it is very popular among people from Asia, so there are many Asian and Indian restaurants. And, Interlaken is not in the mountains. Go to Interlaken if you want to go on another great cruise on Lake Thun (that has a few castles around the lake) or Mt. Brienz (which is famous for its green waters). While staying in Lauterbrunnen, go up to Mürren, Wengen, and Grindelwald. Lauterbrunnen is down in a steep valley, not offering the views that you have from Mürren, for example.
I can also suggest travel forums like the TripAdvisor Switzerland forum. There are locals which can give you great insights on what to undertake on-site.
Best wishes,
Roland