Not likely an O2 sensor, there are separate codes for those and if I remember correctly this car has two, seen those codes too often on that car. I don't think there is otherwise an obvious answer to this one without doing a bunch of troubleshooting. Could be bad injectors, bad coils, bad plugs, bad wires, a dirty MAF or a large vacuum leak etc. The whole issue of things working after 10 minutes would point me more to electrical though, either condensation affecting the wires or coils or a bad connection that rights it self when things expand. In the olden days one would spay WD40 or other moisture dispersants on the high voltage stuff to see if the problem resolved, that is kind of messy and not great for the rubber bits though. You might want to pull boots and stuff to see if there are any carbon traces where things might have been arching. You might want to swap plugs, wires or injectors to see of the problem moves, can't remember if that one had individual coils, is so that's an option also.
Word of caution though, I would not drive the car too much like that in case it is dumping raw fuel into the cat (i.e. the 15MPG thing), it will burn itself up internally and you may need to replace another part...
If you want to swap some stuff I would recommend rockauto.com as a good source of stuff at really good prices. I recently sourced things like OEM O2 sensors and stuff at about 20% of dealer cost for my Nissan. By comparison most of the run of the mill auto parts places I have come across don't seem to have nearly as good a selection of Japanese car parts.
There is another option... Subarus are real enthusiasts cars, there might be a Subaru club near you. Through postings and recommendations on a local club board I found a really good tech to do major work on mine, he had a shop beside is his house, he had been dealer trained, he loved the cars and he was a real straight shooter. You might want to search out a guru like that who won't charge you an arm and a leg and might know what the problem is right away.
