The six travel days are per person. Mexico, Costa Rica, Puerto Rico, etc don't count against them. You have to cross a pond. One flight can count as two travel days if it goes into the next day.

You can interline all you want/have time/money for, but there is an exclusion period from your start date (9 months?) that can differ from airline to airline. If you truly travel a lot you want to go DL on the one day portion and interline on the 2 day segment. A lot of the interline agreements don't put you in first class but if you're good with the crew and purser your odds improve.