I did the same trip but starting from Delhi and ending in Kathmandu, and I
did it in 17 days.
All the different places you're going to see are amazing in their different ways: Delhi with its Moghul architecture and the slums Jaipur - one of the most wonderful places I've ever seen- a country town rich of colours and beautiful people Agra and the magic Taj Mahal Khajuraho - try to see the temples at dawn, less crowd and soft lightning on the stone Varanasi - no place like that can combine bot holiness and misery Kathmandu, a little touristy but very nice to walk around.
I don't think you need too many practical suggestion about food, since tourbooks are full of them, but if you dare try to eat something (cooked, of course) from the street vendors in Jaipur, like roasted meat or made-to-order chapati (indian bread) or honey sweets, you won't regret it. just keep clear of anything you can't cook or peel off. A great experience is vegetarian cuisine, providing you're an adventurous eater and you don't want to understand EXACTLY what's in your plate.
No security problem there, just look out as you do everywhere and, if you wish, keep some coins or small bills at hand for the always present beggars, many children and leprosy-struck ones among them. As anothe Ziner said, you're going to love and hate India at the same time, but you'll experience such a different world you can't find anywhere else and you'll probably come home changed a little inside.