Good itinerary! Few suggestions below:
1. In Agra, you could consider staying at the Jaypee Palace Hotel instead of ITC Mughal. It's a bit dated IMHO
2. Amritsar - depending on your budget, I would suggest staying at The Grand Hotel(close to station) - budget hotel, or The Ista Hotel(boutique) - close to the temple. Either-ways, Amritsar is a small city, and any rickshaw will take you to the temple in a few minutes.
3. In Jaipur - Rajputana is good, but so is the Marriott.
4. Personally I think Varanasi is worth a visit, and do-able in a day. The Ramada Hotel and Radisson Varanasi are good places to stay. However, you will have just under 24 hours to spend with your friends in Pune if you fly VNS-DEL-PNQ on Day 9. So its entirely up to you.
If you need help with booking any of the above, give me a shout. I'm based in Delhi and would be happy to help.
Cheers