Oxidation of fats, if I recall correctly, is still aerobic, but requires more oxygen than oxidation of carbs, so it puts a bigger demand on oxygen problems. My biochemistry is getting rusty though, its worth checking if you think this is important.
Aspirin and similar NSAIDs are the second leading cause of gastrointestinal ulcers. So they should be treated with care. This is because they inhibit synthesis of gastrointestinal eicosanoids, which blocks healing of the gut. So aspirin leads to reduced gut healing. So its good for some things, bad for others, and requires a little care.
Aspirin, I think, is a COX inhibitor, not simply a COX-2 inhibitor. Vioxx was a COX-2 inhibitor, and they were touted as the answer because they did not cause the stomach problems like aspirin did. I think the gut uses COX-1 isoform. Further I think aspirin is a COX suicide inhibitor, which means it does not just suppress COX activity, it destroys it.