Agerys1908 You can easily find the timetables on sbb.ch or in the SBB Mobile App. You have a train from Basel at least every hour to these destinations.
Day 1: You can buy the tickets at vending machines in Basel SBB (French part of the station), on sncf-connect.com or in the SNCF mobile app. It is not necessary to buy these tickets in advance, no reservations are possible.
Day 2 and 3: I suggest to search if Saver Day Passes are available for these days, but be sure to select the full price. With these passes you can take every train on the selected day, but they are not refundable and not exchangeable:
https://sbb-tickets.cc/en/tickets-offers/tickets/day-passes/saver-day-pass.html
The Saver Day Passes are not valid until Jungfraujoch, you must buy additional expensive tickets from Grindelwald or Wengen:
https://www.jungfrau.ch/en-gb/
Seat reservations are recommended for the Jungfraujoch.
They are also not valid for the Pilatus. You must buy additional tickets here:
https://shop.e-guma.ch/pilatus-bahnen/en/tickets
Saver Day Passes are valid for the Mount Rigi, it could be an alternative with the boat from Lucerne to Vitznau.