I had this warranty with my XR6T.I new it wasnt going to last long though due the exact things pointed out by the OP,incorrect oil ect for our climate and vehicle imo.
Part of the deal was that I wanted the car freshly serviced for no extra cost before pick-up/delivery of the BA.This then gave me 3 months to pick on everything possible and get some value out of this "free" warranty.
All up about 4 visits with a few things fixed each time fixed equated to a very anger service manager,I suggested that their car buyers be a little more carefull next time when they trade a car in,look a little harder for faults,not my problem and isnt this what a warranty is for?I'm sure you would do the same if you had mechanical knowledge.He replied,"well I cant answer that question",so I replied with a chuckle"you must drive a Holden"lol.
To the OP,you have made the correct decision by going about things yourself.