Varsha,
--> Not much to add to your TN list - although Madurai and Kodaikanal can be a good visit. Kanyakumari is a little out of the way - but again worth a 1 day trip.
--> since you have mentioned that you want to spend most of your time up north - I'll resist the temptation of recommending the beautiful Kerala
.
--> trust me you aren't missing anything by not going to Bangalore (I'm based outta here) or Hyderabad.
--> There are direct trains from Chennai to Kolkata - I'd advise you travel in AC coaches - the journey is around 36 hrs long.
--> Darjeeling is very well connected with Kolkata. Regular buses and taxis ply on the route. The Toy Train from Siliguri to Darjeeling is a good experience.
--> There are numerous trains going from Kolkata to Varanasi.
--> Lucknow is connected by Bus/Train to Varanasi - don't miss the famous Tunday Kababs
--> Agra, again is well-connected with Lucknow by bus/train/taxis etc
--> Agra to Delhi is a 4-5 hrs train ride - worth trying the chaats at chandni chowk/paranthe wali gali and Karim's non-veg preparations.
--> I'd advise you to drop Shimla and go to Manali-Manikaran (hot water springs)/Dharamshala instead. Shimla is just too touristy. Overnight buses from delhi are the best way.
--> I am not a 100% sure whether there're direct comfy buses from Manali/Shimla to Amritsar. There might be some govt buses though.
--> Attari (border with Pakistan to see the ceremony) is a day trip from Amritsar
--> Either come back to Delhi and then go to Jaipur on the Volvos running from Bikaner House or take a bus/train from Amritsar - worth trying the chilly pakodas (fries) in Jaipur
--> Most/All of these places are connected by overnight trains with each other - Jaisalmer Jodhpur Mt Abu Udaipur
--> Ahmedabad
--> Mumbai
1) Do the above places look feasible for our time frame? -- Yes the places are feasible - depending upon how much time you wish to spend in each place.
2) Have we missed out any "must see places" along our route? -- Not really. Goa isn't the same place during off-season. Again, Kerala, if you can.
3) Any places not worth considering? -- kolkata and darjeeling - don't see the point - unless you want to visit Missionaries of Charity office and see Tea Plantations. And Ahmedabad
4) Are there any flights for our route that we should look into booking now to get cheap fares? Maybe Chennai-Kolkata? -- Chennai - Kolkata should be a cheap flight if you book well in advance. Otherwise your route is perfect for a train journey - book in advance
5) Any hill-stations ok in March/April along our route? Would be nice to see some of the Himalayas.... -- Kumaon/Garhwal in the lower reaches of the Himalaya are good and well connected with Delhi / Lucknow - Nainital/Saattal/Baageshwar or Pindari Glaciers in Kumaon; Hrishikesh/Badrinath/Kedarnath in Garhwal. I agree with Arif, Sikkim is another option
Let us know if you need further guidance.
Have a good one!
Apurva