<<"Please advise what is the best option as regards rail pass, which one to buy ? Also for the Rhine falls do we just go there and buy the tickets or do we book a tour ? For Mt Titlis, do we just buy tickets and go there or do we book through an agent ? What is the best option ? ">>
These links will help you to better understand your options:
I defer to the moderators when it comes to "Which pass?"
They know a lot more about rail passes than I do.
It is not necessary in either case to book a tour, and you'll have more flexibility to explore at your leisure, because of frequent transport service, which you can find in the timetable:
There are frequent trains from Neuhausen Rheinfall to Luzern. The fastest depart at xx01, change at Zürich and take 1 hour and 48 minutes.
There is also a bus to Schaffhausen, followed by train via Zürich, and some other options which you can explore with the timetable.
From your plans, it seems that you recognize that the Rhine Falls will not require a full day to explore.
If you go to Luzern as planned, you'll have some time to explore the city:
There is a lot to see, and that would make a good day.
However, with hourly service to/from Luzern /Engelberg ( base for Titlis) taking about 50 minutes or less, you might find time to see a bit of Luzern on the 28th.
So, I wondered about fitting in a trip to Stein am Rhein while you were in the area of the Rhine Falls, and it could be done. it would take quite a while to reach Stein, and you'd not have a lot of time there ( and, it is not really needed). The return from Stein to Luzern takes about 2 hrs 20 minutes. You'd get to Luzern for dinner, but it would be a rather full day. It would be more relaxing to follow your plan as written.
By the way, many people really enjoy the Rhine Falls. They are powerful, and you can get close if you wish. Personally, I have seen a lot of waterfalls, and prefer to spend my time in Switzerland exploring things that are more uniquely Swiss. Nonetheless, it does fit nicely into your itinerary.
Here is more information about Titlis, to help you understand what you can do and see there: