First know that you need a valid Indian tourist visa to leave the international transfer area of the terminal. An eTV (for many nationalities) can be applied for online for this, without going to your embassy, although these are single-entry: i.e. your shopping trip uses up the entire validity of the visa.
Second know that Delhi airport is a 70-120 minute drive to downtown New Delhi at most times of day. Each way.
Answers to your questions:
Passport (containing your Indian visa) and boarding card to KTM should be sufficient to get into the airport.
If you bought both legs on the same ticket, they probably will transfer the luggage, but definitely confirm this upon check-in in London. If you bought them on different tickets it's quite unlikely that they'll transfer for you.
No problem to stay in the transfer area of the international terminal. Since it's a <24hr layover you don't even need an India visa in this case.
There are currency exchange places in the airport, after Indian immigration. There are also ATMs there to give you rupees, and the airport ones are kept well-stocked with cash (you will have better luck here than at ATMs in the city, given demand for India's brand new banknotes)