1. TK is not a US domestic carrier, there are almost never ever paid upgrades "at the gate". I have seen this perhaps twice in over 600 TK flights. At ticket desks and airport check in's is where it is most likely to be a possibility, (or at OLCI) however you are never going to be offered less than 45k, and could easily be offered $999-$1599 for the segment in cash.
2. As mentioned by others 45k is what it costs and it will never be less.
3. Maybe you can get the to tag the TBS segment on, but it is doubtful.
4. Sk AAR's theory is nice, but good luck in getting that for 45k if you tried it, it could be 180k or whatever.