Given what you've said above (including your mention of Kingfisher as the connecting intra-India segment):

1. There is a transfer waiting area and free transfer bus available just after you claim your bags at DEL and clear Customs. After passing the customs exit where you hand a small customs chit that declares your total count of luggage, the transit lounge bus waiting area is on your left side -- it's just before the area where the hotel drivers are waiting with placards with guest names on them, so if you have gone that far, you've gone too far and should back up a bit.

2. You have to clear arrival passport control at DEL. The security check of luggage and person for departure from DEL to Amritsar is done just once.

3. No immigration formalities in Amritsar are involved unless talking about some kind of extra registration required for a limited set of foreign nationalities or otherwise staying for more than a few months time -- and even that is not done at the airport ordinarily.

4. Kingfisher ordinarily has been allowing me two free checked bags within India as long as I show them my same day or previous night boarding pass. Even if hit with excess baggage charges, they are pretty reasonable compared to what is charged within the US/Canada or for international travel.