1.) What would be the best currency to use for international transfers from the US to places like India, North Korea, the Middle East.
The use of the USD is favorable on India and the Middle East except the bolded part. Idk what currency are they exactly okay with or whether they accept any other nation's currency but your best bet is to just use bitcoin in NoKor (if ever you are really deep into this one) due to their recent involvement with such. IIRC, Hong Kong and Macau were the gateways of money transfers if you want to send money over at NoKor (though of course, why would one do that?)
2.) How could the recipients turn their crypto into cash without going through a bank? For example, if we sent 10,000 worth of Rupee to India via crypto, how would the end user convert this into Rupee in their country?
Facilitation of OTC trades and the use of P2P exchanges would do the trick, however this is not 2013-2014 anymore and most exchanges and methods of converting crypto to fiat are being regulated, and so one should really get into the official process in order for them to get their money.
Or a not-so-popular option: use this forum on the Currency Exchange section and post trades in there. Perhaps you might get lucky and get someone who would want crypto in exchange for cash.