I had a tough time getting back my refund as flight was cancelled. Flight cancellation hassle was due to airline which was a different story, but they surely did not help in refund. Finally got refund after 4 months.
Cant comment on other aspects but getting Refund from them was painful and difficult, to say the least.

MakeMyTrip is basically India based, but yes they should be having an office in the USA, but I'm not sure.

I did have a problem with them for my Hotel booking, but I got the refund in less than 15 days. I'm very HAPPY with their service.

They are india based but do have a presence in USA, you can look for the US website. They have abysmal customer service when the need arises. I would hunt on the airline websites directly, the prices will most likely be the same. Hope that helps.