Needs help to plan tour program and rail pass

Hi poonam, and welcome. You can cover your visits as follows: lake Thun, Bern and the Jungfraujoch can best be reached from Interlaken. Lucerne is the best base for a visit to Engelberg and the Titlis. I think you listed great ideas for your itinerary, so I don't have that much to add. When you're in Lucerne, you could also visit the Pilatus (which is very close to Lucerne) and combine this with a boat ride over lake Lucerne. As for things to see and do around Interlaken: the Bernese Oberland day trip overview lists many tips. The timetable is a great help in planning your trips.

A rail pass will definitely save you money. Which pass is best, however, depends on your exact travel plans. Our FAQ may help you out in calculating which pass is the most economical solution. An 8 day Swiss Saver Pass is in any case the easiest solution, as it allows unlimited travel in trains, buses and boats (including boats on lake Thun and lake Lucerne) and discounts for mountain transportation on all days of your stay.