Does a frittata have to be baked?

Yes you do need to cook the top for the eggs to set, but if you have a large lid reduce the heat an cover and check from time to time until the eggs are set

It depends on what you have in the frittata as you want everything to be cooked at about the same speed.

Basically you are turning a fry-up into a frittata by adding the eggs

Dune

Definitely not. The first frittata that I saw an Italian chef prepare was many years ago and she did not put it in the oven. The traditional method for flipping the frittata over is not so easy which is why so many people finish it under the broiler or in the oven You need to be quick and careful. Using a flat dish that is larger than your pan pan or skillet, (a round pizza pan works too) place one hand firmly on top of the plate and the other hand on the handle, now quickly turn the whole arrangement upside down. Immediately slide the frittata back into the pan The golden-brown cooked side will now appear on top. Finish cooking the frittata on the stove until the bottom is also golden brown. Now if you are really good, you can just flip the entire affair so the top is on the bottom.

No you can place it in the skillet

yes, otherwise you are making an omelette