Hi Ashasvi -
You can check a trip to Salzburg on the timetable linked above.
Trains from Zürich to Salzburg are frequent, with one or two changes. Time required ranges from 5 hr 23 minutes to 6 hrs 19 minutes.
How much time do you plan to spend in Salzburg?
Actually, your list of Swiss activities that you hope to do is going to be difficult to fit into the time allotted.
An approach to consider is to open up this map:
Pick out the cities that you mentioned. (I like to do it on a paper map....)
Also, using the links in My Swiss Alps that describe the scenic rail journeys, such as the Glacier Express, you can place the route on the map.
www.myswissalps.com/gl acierexpress/gettingth ere
Look under the tab for Route, and scroll down.
Then start thinking about some rational route for connecting your targets. The timetable tells you about journey times.
The nice thing about that particular map is that, if you zoom in to zoom level 32, the train lines pop up very clearly.
Under Points of Interest/Traffic, in the menus, turn on Trains(optionally, buses, trams, mountain transport).. Icons for train stations pop up. Mouse over them. You get the exact name of the station, which you can enter in the timetable for a start or destination. You don't need that for major cities, but if you want a suburban station or a stop on a cableway in the Alps, you can get a name for it. Or, a boat landing.
Also, as you do that exercise, its can lead to discussions about which places are more important.
This page can help with that: