Hi, I'm planning a trip with my parents and this is the tentative itinerary -

1. Arrive in Munich on 25 Apr, Saturday from New Delhi.
2. Leave Munich on 27 morning and arrive in Zurich. See lake zurich, old market etc.
3. Leave Zurich on 29 morning and arrive in Interlaken. Visit interlaken and joungfrau for 2 days.
4. Leave Interlaken on 1st afternoon and go to chur. Stay the night in chur.
5. On 2nd May, take the bernina express from Chur to Lugano (UNESCO heritage train route through the alps). Take the train from Lugano to Rome . Reach Rome at 11:30pm.
6. 3rd May-5th May Spend in Rome.
7. On 5th May evening, take the Thello night train from Rome to Paris (or take a flight to Paris.)
8. Spend 6,7,8 in Paris and leave 8th evening from Paris-CDG to New Delhi.

Does the itinerary have any problems or red flags? Also, will getting a 4-Country family Eurail pass (6 day duration - for the intercity train/bus travel) be a good idea? It costs 1155 euros after discounts. What is the cheapest way to book hotels (Holiday inn type should be good enough)?

Far too rushed. You aren't allowing enough time in locations to actually see things. Too much time spent on transport rather than seeing locations.

Skip Zurich and the Bernese Oberland and visit the Engadin instead: tons of glaciers and high mountains too.
Leave Munich at 9.00 by http://meinfernbus.de/en to Chur ar 13.00. Fare: 18 EUR/pax. Put your luggage in the railway station lockers, have lunch and visit this historic Swiss town.
After that, take a train to the Engadin Valley (2 hrs ride, northern leg og the Bernina Express line) and sleep there (Pontresina, Sils Maria or so).
The following day, take a gondola to Diavolezza, in the middle of glaciers or to Corvatsch, a similar peak.
http://www.diavolezza.ch/en/ Have a look at the video
Continue one day later by Bernina Express to Tirano and by Bernina Express bus to Lugano.
Stay a full day in the Swiss town of Lugano, enjoy the Lake and the cableways to the neighbouring hills (panorama to the Alps!).
Proceed then to Rome, but don't take the very last train. Leave Lugano rather at 16.26 and arrive at Rome at 20.55.
In this way, you get 2 more days for Munich and Rome.