Feb/March should be great in South America.
You can stay in touch pretty well with just your iPhone or an iPod Touch - make sure to shut off things so you don't get charged for data, etc. There are apps for Skype, etc. to call home cheap while on Wifi, and you can definitely email that way.
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I agree with traveling light. In terms of washing clothes, you can use regular old shampoo as detergent in your hotel room sink - it gives the laundered clothing a nice scent, too. Some clothes dry more easily than others, though. One trick for drying is to roll up the wet laundry in towels, then step on the roll to help dry the clothes. Get a flat rubber round stopper for sinks, as they don't always have them. Your hotels will also know where cheap lavanderias are.
You can find decent little places to stay in Easter Island from locals, who show up at the airport with pictures of their lodgings, often with breakfast supplied. Should be able to get a decent spot for less than $45 a night or so. Supplies on Easter Island are a little harder to come by.....
One tip for Buenos Aires is to go on these free walking tours - just tip the great guides a few bucks at the end. You will have a great time, and get a idea what you want to go back and visit on your own later.
http://www.tripadvisor.com/Attractio..._District.html
(Do both the tours, they take in different parts of the city.)
RE: Time in Peru- I really suggest you go to Cuzco to see the Inca ruins and Spanish colonial architecture. You might be pushing it to try to get to Macchu Pichhu, though that can be done in a single day train trip from Cuzco, and is a one of kind place. Not sure that you need more than a day in Lima, though others may suggest differently.
Have a great time. I'm jealous!
Add: As far as "sticking out" as an American, one really doesn't in Argentina at all. You will be assumed to be local, and spoken to in Spanish, with many folks able to switch to English without a hitch. Chile is much the same, as is Lima. When you get to the tourist areas in Peru, they are more geared to recognizing travelers. Easter Island is such a small place that I think everyone knows everyone else who lives there.
Any big city, be it in the US or in South America or elsewhere, is going to have those who seek out the bewildered looking and might try to take advantage. A money belt or pocket hanging around your neck or inside your clothing is a good precaution in any big city where you might be amongst crowds. Learn a little Spanish, meet some nice people, have some great meals (wonderful ceviche in Peru/Chile, wonderful beef in Argentina, etc.) and have a great time.