It's a LONE4 going from EUR-SA-NA-Asia-EUR

This is what I have so far:
x=stopover
//=transit

LHR-x(GRU)-EZE-SCL-IPC-SCL-LIM-JFK//BOS-CUN-BOS

then I'm not sure for the rest of NA..

JFK-NRT-x(TPE)-HKG-PEK-HKG-x(BKK)-SIN-FRA//MAD-CAI//TLV-MAD-ATH-LHR

It's not particular good use of accumulating miles but it gets where I want to go.

Basically, 2nd term doesn't start until February 7th (thank you January Term ) so I want to start in London after Christmas and do the South America portion during January, then head up to NA, utilize the BOS-CUN-BOS legs for Spring Break in March (I figure you have to do the college CUN thing once...) then after graduation go to Asia and the Middle East.

So some questions:
1) Is what I have so far legal?
2) Any suggestions for NA?
3) Any suggestions for improving overall? (Better mileage accumation, Better places to go, etc..)

I'd like to go to IST too, but maybe I can plan that outside the RTW journey...
I'd start in CAI if i could find a cheap way of getting there to better utilize BA in Europe