Olive oil is best eaten raw and should be organic extra virgin and cold pressed. This oil must never be used for frying. We only use it for making salad dressing. Stay away from all other vegetable fats (except coconut oil) as they have been processed and very unhealthy.
We fry food all the time but use bacon fat, beef lard, butter and coconut oil. These are very healthy fats that are perfect for high temp cooking. Your body needs lots of good fat.
We only steam a few vegetables but prefer foods fried, stir fried, roasted and making heavy stews. We also use lots of butter on our vegetables when they are steamed or boiled.
That is great you are avoiding sugar. Probably the worst substance on the planet for people to consume.