What exactly does Cleartrip mean when they say they have designed a multi-city itinerary by combining multiple one-way flight tickets?

I am considering the following multi-city itinerary:
Leg 1) JFK-KBP-DEL on PS
5 hours in DEL
Leg 2) DEL-HYD on 6E
[unusual but please don't ask why]

Can I check in luggage at JFK all the way to HYD? If I miss the connection in DEL (5 hours), is Cleartrip or Ukraine Airlines responsible for putting me on the next flight to HYD?