Except that you are interested in trekking/mountains, I d choose Rajasthan over Nepal. In Rajasthan go to Jodhpur, Udaipur and Jaisalmer. Not a big fan of
Jaipur.

Try go to Varanasi. It is the the quintessencial Indian city and a fantastic spot for pictures.

I am not a fan of Agra but I guess you would like to see the Taj Mahal.

I must admit that I feel envy. I wish I could experience India for the first time again. It is a fascinating country. You ll probably regret your decision the first few days though.

Yes it is frustrating sometimes but it is fascinating.

Travel by train is totally fine. I have even used Sleeper Class once and it was Ok. Given the choice, I d go with AC2 though.

I would avoid Delhi in winter and during the Monsoon season. I don t mind heat but summers temperatures are normally over 40C.