Hi Anjan-
Sounds like a nice trip, if a brief one.
I've not got answers to all of your questions, but here is a start.
<<"There isone Eurocity train from Basel to Luzern at 14.04 hrs. Shall we have to buy any ticket for the journey?">>
If you have a Swiss Travel Pass, you do not need to purchase tickets. The pass does it all, inside Switzerland.
And, to understand your journeys better and answer questions about the journeys, , use the SBB (Swiss Rail ) timetable. If you follow the links, especially the "+" sign to the left of each journey after you have identified the journeys, quite a few details become visible.
This link about the timetable in My Swiss Alps gives lot of useful tips on using the timetable, and will help with your questions about rail journeys. The timetable is full of information, but takes a bit of digging to get at some of the more useful material:
www.myswissalps.com/ti metable
If you wish to visit the Rhinefalls, here is a helpful link:
www.myswissalps.com/rh inefalls
I think it is a bit of a stretch to fit it into your short stay. You have identified some nice things near Luzern (the German spelling of the name, which you will see in that area of Switzerland) and their are plenty more to fill your time.
The timetable will help you determine the time needed, and the link will give you directions on which stations you can use.
This map is also useful to visualize your journeys. I think it can help you a lot, since some of your ideas show a mix up of the various possible trips.
It shows the rail routes; zoom in.
map.search.ch/?x=8592m&y=50256m&z=2
If you zoom in and turn on "Traffic" under the "Points of Interest" menu, you can see the train stations, etc.
<<"2) On 06.07.2016, in the morning session, we shall visit Mt Pilatus, by taking boat to Vitznau. In the evening session, we shall try to visit Mt Rigi.
3) On 07.07.2016, we shall try to go to Mt Titlis, via Alpnachstad by boat. In the evening, we shall go to Interlaken Ost by Golden Pass train.
a) How we can find it in timetable?">>
Item #2- The boat to Vitznau is used to go to the Rigi. You can do both Rigi and Pilatus in the same day, with careful planning, but please watch the timetable carefully. Trains/cableways down from the mountains do not run at all late in the evening. Boat trips also are less frequent.
Check these links-
www.myswissalps.com/pi latus
www.myswissalps.com/ri gi
www.myswissalps.com/ti tlis
The map that I linked to above will be particularly useful for both the Rigi and Pilatus, because there are choices for how to go up and come down each mountain. Please note that Alpnachstad is the base station for the cograil train to Pilatus.
Item #3
Alpnachstad is not on the route to Titlis. The route to Engelberg and Titlis goes through Stans and Dallenwil. Please zoom in and look at the map I have linked to: Here is the partially zoomed in link with railway stations only turned on in Points of Interest:
map.search.ch/?x=8304m&y=11472m&z=32& poi=zug
<<"There isone Eurocity train from Basel to Luzern at 14.04 hrs. Shall we have to buy any ticket for the journey?">>
Trying to fit in a trip to Interlaken Ost is technically possible, if you don't spend much time at Titlis, but you will not have time to do any sightseeing in the truly Alpine villages ( Grindelwald, Lauterbrunnen, Wengen, Mürren) south of Interlaken. Interlaken itself is not much of a tourist destination. It is more of a base city and transfer hub.
Check this link:
www.myswissalps.com/ju ngfrauregion
Regarding your connection in Milano Centrale, I personally would book a longer connection. However, I cannot predict whether your connection will definitely be OK or definitely not be OK. People reporting in this forum have had success with such short connections at Milano Centrale. Remember that, if your incoming train is late, your outgoing train may well be, also.
In Switzerland, 4 -6 minute connections are common and are reliable, and possible.
If you have a lot of heavy luggage, that will slow you down on the transfers; travel as light as possible.
I would spend some time with station maps and track numbers for arrival and departure ( which are usually available from the Swiss Timetable; hopefully, they are reliable in Italy. They certainly are in Switzerland.)
Hope that helps.
Slowpoke
