>> Regarding the one day trip to Schilthorn (and Murren), is it is it worth the effort? It's too far away from Lucerne and back, 4-5 hours approximately?
Mürren is a lovely village in a stunning location if the weather is clear. If the valley is filled with fog, the village is still charming, but you won't have any views.
The Schilthorn is also a great trip with wonderful 360 degree views of the mountains if the weather is clear. In 2018, the Schilthorn cable car is free with the Swiss Travel Pass.
Mürren, and its views, is very unlike what you will see in Luzern.
Whether the travel time is worthwhile is something to decide for yourself :-)
>> How can i check the weather before the trips to the mountains? from a specific site?
Check the weather the day before, and the webcams on the day you intend to go. Sunrise is between approximately 6:30 and 7:00 in March (note: clocks go forward an hour on Sun 25 March). One disadvantage in travelling from Luzern is that the weather can change between when you check the webcam and when you arrive in Mürren.
>> The Engelberg to Brunni cableway -> what is that trip?
It's a cableway in Engelberg (not part of the cableway to Titlis).
>> The Vitznau to Rigi Scheidegg cableway --> is the journey to the top of mt Rigi?
No. The top of the Rigi is Rigi Kulm. Rigi Scheidegg is a lower peak elsewhere on the Rigi massif. For the various options to get up to Rigi Kulm (which are all free with the Swiss Travel Pass), see here:
>> is it worth or mt Pilatus and Titlis are better options near Lucerne?
They are all beautiful and all worth it. If you don't have enough time to do them all, opinions will vary on which is best. Read the information (including about the Rigi via the link above) and decide what's right for you.
The weather and cloud cover/fog on the day might end up being the deciding factor - check the webcams before choosing.
Webcams Pilatus, Rigi, Titlis