Yes. With United miles you can book the following itinerary but must be booked as a roundtrip. Neither UA or AA provides a very luxurious first class experience on this route, so don't get too excited.

EWR - LIM

Week layover LIM - CUZ

CUZ - EWR.

Yes you have to take a train to MP. Actually you have to take a 2-3 bus ride from Cusco to the train station, and then about a 2-3 hours train ride to Aguas Calientes and then from there a short 30 minute bus ride to the top of MP. It is a lot of traveling- but every step is scenic and breathtaking (I mean that literally and figuratively- very high elevation!)

It isn't the easiest route in the world but in Cusco there will be a ton of people selling packages to MP which include tickets into MP, train tickets, overnight in a hotel and bus ride to the train station for around $200 per person (purchase this at the Plaza de Armas- main square). I would buy this in Cusco as it is very convenient and everything is taken care of for you.

Enjoy