Hi Dipankar -
Thanks for the updates.
I was afraid you might be going in early June, which might be summer down in the lower elevations, but, for sure, not up on the Jungfrau.
In August you will certainly have all of the tourist facilities, services and cableways leading to scenic spots and hikes open and running. It is the height of the tourist season, so everyone is eager to serve the tourists and earn a living. ;-)
I think Annika's idea about going through Montreux on your way to the Berner Oberland makes a lot of sense. After Montreux, you could ride the trains on the Golden Pass Route from Montreux to Interlaken, for example. In the timetable, you have to force the journey through Zweisimmen, or else it will go through Visp.
(There is an alternate, slower, very scenic route through Brig and Kandersteg, if you really want to ride trains and see mountains. Let me know if that interests you. You could have time to do it.)
Also, I see that you have decided to spend more time in the Alps or near them at Luzern and Interlaken. You did what I would have done if I were pressed for time and wanted to se he Alps....you skipped the Rhine Falls. I think that is a good idea, personally. They are nice, but they are not the Alps. ;-)
I'd take as much time in or near Interlaken as possible (unless the weather is very cloudy, when I would cut back a bit), but still give Luzern a couple of nights.
See attached screen grabs.