Just got back from 4 months backpacking SA, been to all the countries you are going and more. Your itinerary is really packed for a 20 days trip, leaving no room for error (plane/train/bus delays, which is pretty common.) bring USD to change or draw local currencies from ATM there if you are uncomfortable with bringing lots of money around. ( All the ATMS IN SA accept our debit cards with either cirrus or visa plus logos, a small service fee applies for each withdrawal though). Get the yellow fever vaccination at TTSH travel clinic, but no1 really check throughout our trip. Haha)
A few suggestion on itinerary:
1) you allocated 1 day to see Iguazu fall, might not be enough if want to view it both from the Argentina side and Brazil side, both are equally spectacular and different views.
2) Cusco is a nice little town with plenty to do and a good place to acclimatized to the high attitude of Peru, especially you are coming in from Singapore and Brazil which is almost sea level. Good to leave 1 full day for acclimatization for the body before leaving for Machu Picchu. Not much to do in Lima, so if your itinerary are pretty much fixed, I suggest you spend 1 more day in Cusco instead of Lima.
3) Easter island. You have 3days 2 nights. Basically 1 full day. Suggest you rent a car in the town (50usd/day) and drive to all the archeological sites to see as much as you can cos it really amazing.
4) Santiago: if you have time, take a bus to Valparaiso. A beautiful city nearby. If you are into street arts, this is the perfect place.
5) free walking tours: there are many free walking tours in SA. The ones in Santiago and Cusco are pretty good. Go google when you reach a new city. No better way to explore a new place than with a local. And a really good way to meet fellow travellers.
If somehow your itinerary is flexible and you are able to extend your travel, check out Patagonia area of Argentina and Chile, most amazing scenarios and hikes. And one of favorite countries in SA, Colombia.
Enjoy Latin America!
