Deep Frying in an electric skillet can be done but it poses a risk of fire from the cooking oil.
If you put too much cooking oil into the electric skillet then it may come out of the skillet and cause a fire.
But you can fry foods in the electric skillet by filling it with a little oil and then placing the food into the electric skillet.
I've fried potatoes, hotdogs, chicken, Turkey etc in my electric skillet and it turned out just fine.
Although I've never actually deep fried with my electric skillet.
I would recommend just getting a cheap electric deep fryer to deep fry foods more safely.
Electric frying pans are good for cooking in.
If you just want to cook something and don't want to use the stove or you don't have a stove then an electric frying pan is a good option.
An electric frying pan cooks a bit slower than a stove does but it's still a good thing to have and I've used electric frying pans in a dorm room before.
You can fry potatoes, hamburgers, fry eggs, make scrambled eggs, pancakes etc in the electric frying pan.
You just have to wait a bit longer for the food to cook but the electric frying pan does cook the food just fine.
Chicken can also be fried in the electric frying pan.
An electric frying pan uses between 800 to 1000 watts of electricity and are pretty cheap to use.