Sorry about so many questions here. I've done some searching and re a couple of my questions have looked through visa info sites of Delta and a visa processing service I usually use, but could still use some advice and info:

1. In mid-March I may overnight in DEL flying between San Francisco and Kabul. If arriving on AA, the overnight would be on the outbound for about 15 hours; if on BA, the overnight would be on the return for about 8 or 12 hours. Air India between DEL and KBL. FWIW, the tickets would be in J. Is the airport transit hotel open yet? If so, would I need to clear immigration and security in transiting from AA or BA to AI?
2. If I do need to clear immigration and security, am I correct in assuming that I would need a visa (I am a US citizen, not of Indian origin)? And if so, is there a transit visa or would I need a regular tourist (or other) visa?
3. If the airport transit hotel is not open yet, what are the best nearby options for overnighting?
4. There is also a chance that I will need to attend a conference in New Delhi in late February. If I correctly understand the rules, it is possible to get a multiple entry visa, but one cannot re-enter the country within two months of leaving it. So what is the best process to follow in the event that I need to visit the country in late February and then pass through again in March.
5. If because of the multiple entry problem I might want or need to remain within the airport and the transit hotel there is not yet open, are there any lounges or other options for grabbing a shower and sleeping through the night there?

FWIW, instead of passing through DEL in March I could possible route through Dubai to get to Kabul. But for various mundane (though not on FT!) reasons--mileage accrual, upgrade possibilities, price--I might prefer DEL if possible.

Thanks for any advice and info!