To get smaller particles you have to do some work, whether inside your stomach or outside of it. When you eat cold whole oatmeal with milk then bigger colder particles reach your stomach which then will have to perform more work, spend more energy, on breaking that down than when you, say, eat finely-ground porridge that you have cooked for a minute with the same amount of milk. How will that not be different for the body? Of course you can always define 'nutritional effect' such that by definition such effects are excluded but that's probably no what you want to say.
Thermic effects of food are very marginal. Especially if you’re comparing something like oats and finely ground oatmeal instead of two wildly different foods like oats vs meat. I’d suspect the difference is at most 5%, likely much lower, which is within the margin of error for caloric reporting of labels. Humans are very efficient at extracting nutrition from food.
No. Diet Induced Thermogenesis (DIT) can vary from 0-3% (for fat) to 20-30% (for proteins). Carbs usually vary between 5 and 30%, depending on the amount of fiber. A fiber-rich oat would likely be around 30%,and a fiberless oatmeal 10-20%.
Please read the context again. If the only difference is oats vs finer ground oats, fiber would not be removed and nutrition content would be the same. Simply grinding up something doesn’t destroy its fiber content. If there’s additional processing to remove something such as fiber content then that would have an effect, but now we’re not just making particles smaller.