Hi P1 -
<<"For 2nd day in Lucerne i am planning to Mt. Titlis as mentioned earlier, what would be the journey time .">>
Please refer to the timetable link that Annika gave you in the answer to Q1 in her post.
When I do that, using Kleintitlis as the destination, I get 1 hour and 53 minutes for the trip, of which the first 53 minutes are used to reach Engelberg.
<<"I don't want to miss to visit MAISON CAILLER chocolate factory in Broc.">>
You will find information about Cailler at this link. The train station is shown as Broc-Fabrique on the map at this link.
Using the timetable, with stations Interlaken Ost and Broc-Fabrique, the journey is shown to take 1 hrs 24 minutes. [Corrected in Edit - 2 hrs 24 minutes!] Change trains at Bern and Bulle. If you select a journey and Show Details, you can select a map, which reveals a rather roundabout journey.
If you force the computer to show the more direct ( but much slower )route by inserting Zweisimmen in the "via" box, the map will show you a route which follows the Golden Pass route as far as Montbovon, then turns north. The most scenic part of the Golden Pass route is the last section from Montbovon to Montreux. You would miss it. The journey takes from 3 hrs 16 minutes to 3hrs 55 minutes.
As part of your trip planning, you might find a map of Switzerland useful.
Here is one that I use:
Being somewhat conservative, i prefer the older"classic" version, but either one is good. it gives me a menu of options on the very first page. Probably too much info for a smartphone screen? I like it for my computer.
Arno and Annika are better qualified than I am to answer your more detailed questions. However, if you use the tools that have been suggested, you will be able to focus your journey and your questions more easily.
The Swiss Travel Pass only covers travel to the border. You need another ticket from the Swiss border to Paris.
In the lower elevations, you will find that Spring is well advanced in April. In the higher elevations ( Jungfraujoch, Kleine Scheidegg, Männlichen) there will be plenty of Winter still there.