HIP = Higher intermediate point

This is a fare check in a R/T ticket that will raise the fare to that between the origin and some point other than the turnaround point if there is a stop on the trip and the fare between that point and the origin is higher than the fare to the turnaround point. -- Aren't you sorry you asked.

You can't do both CAI and DME from LHR on a OWE ticket so the Moscow trip would have to be separate if you start in CAI.

You run the risk of the airline coming after you for additional fares if you throw away the WLG-CAI(LHR) segments. May not happen but it is a risk.

You can transit North America when going between South America and another continent even if you have been to NA previously. Note that transit means a less than 24 hour stopover. Get a new agent!