If less than 24 hours it is not an stop-over; it is a connection.

Good luck in trying to convince an Eurobonus agent to allow you to criss-cross N A or S America to get from CUN to ARN. You will be allowed to transfer at MEX or a US gateway and in Europe if you can't get on a SK flight to ARN - and that is it. I doubt an agent will allow you to fly via BOG on AV if other more direct options are available - but by all means try it.

Yes, I believe the taxes and fuel charges are higher for LH flights.

Don't believe everything you read. Lufthansa is perfectly OK, in particular if you are afraid of narrow "coffin" like seats.

No, I have yet to try the new TK J seats, but I hardly can't imagine that I will not be pleased with TK (it is one of my favorite airlines; in particular in Y the service is way ahead of other carriers). I don't mind narrow seats (actually I prefer privacy than more open J seats).

Did you check availability? When searching for award tickets in business class it is often not a question of which airline you prefer, but which airline has seats available for redemption. If you believe that you be able to select from all * A carriers flying between CUN and ARN I'm afraid that you will be very disappointed when you actually try to book your award ticket - but I guess you will find out once you try to book. Most often it is a matter of taking the seats that is actually available in J, not which carrier to choose from.