Here's a fairly fully utilized itin that covers a fair few of the places you have mentioned: http://slfft.allhyper.com/0.95/award...CT-LHR-MRU-JNB.

Saint Lucia is a fun stop-off on the way from JFK to MIA & is over 2000 miles from JFK. I've also taken the liberty of substituting MCT for DXB. That's only 'coz I think that DXB isn't worth seeing when you compare it with MCT, but DXB would work just as well.

About question 4., I'd be inclined to call the RTW desk, but ask them about queueing it to AA London for ticketing. With the new EU rule, this might save some problems & you should get the same price, converted to GBP. (Might also save a %age currency exchange fee on your credit card .)