Hi supeng, and welcome to MySwissAlps!
>> I just got to know about Tell Pass Summer. Can I ask if I am able to use this pass from Zurich to Lucerne and back to Zurich.
Coming from Zürich, the Tell-Pass is valid from Baar (if your train stops there) or else Zug, so you need a separate ticket from Zürich to Baar or Zug.
You can download a map showing where the Tell-Pass is valid:
>> I am thinking of going to Mount Titlis from Zurich. From the website, Tell Pass covers Mount Titlis cable car ride.
Yes, free with the Tell-Pass, but you will need to present your Tell-Pass at the Titlis valley station ticket window to get a free bar-coded ticket for the gondola barrier gates.
>> What about the train ride from Lucerne to Engelberg and back to Lucerne?
Yes, free with the Tell-Pass.
>> Is it worthwhile using this pass as compared to taking a day tour from one of the tour operators?
In my opinion, definitely yes, if you make the best use of it. It is available for a minimum period of 2 consecutive days.
>> Is it doable to do Mount Titlis from Zurich?
Yes, it will take about 2.5 hours to get to the top of Titlis from Zürich. It would be much better to stay in Luzern so you can make the best use of the Tell-Pass by visiting other attractions without losing the travel time between Zürich and Luzern every day.
>> Besides Mount Titlis, a friend has recommended Mount Rigi. Can I use this Pass to go Mount Rigi from Lucerne.
There is a lot to do in Luzern. Reading this page in conjunction with information about the Tell-Pass will help you discover more: