I cannot understand how to properly fry seafood

Given your picture, I think the correct term here is saute; that is, to quickly fry in a little bit of hot fat. Pan frying uses more fat, and a lower temperature, to create a deeper crust. Probably an overkill for mussels.

For a saute, you want relatively dry (pat dry with towel if necessary - frozen seafood can release a lot of water) ingredients, relatively high heat, and a solid pan that is not over-crowded. Heat the pan, add the fat, then the ingredients. Then generally keep the ingredients moving during the cooking. Here is some further direction that details the process.

See also this for a discussion of the origin and use of term/technique.

You say

In the advertisements the chefs just swirl the mussels, shrimps, and octopus pieces around and produce some tasty browned pieces

That's like saying "When I watch Bob Ross, he just puts paint on the brush, then moves the brush on the canvas, and a landscape emerges. I tried it and no landscape came out."

What you are missing is not theoretical knowledge, but a skill. You are doing the proper steps of the process, in the proper order, but what you cannot do as a novice is to control the relevant process variables, in this case heat transfer. To become like those chefs, there is nothing you need to understand. Rather, you need to invest a few hundred to a few thousand hours of deliberate practice until you start doing it properly. The unconscious part of your brain has to learn to recognize when the food is being heated properly, and when it is the time to intervene.

The process can be shortened if you can be an "apprentice", in the sense of watching somebody do it, then trying it yourself and having them correct you as needed. If not, you can still learn it, you just have to be more concentrated and accept more errors in the trial-and-error process. Until then, you have to eat the food as it comes out of your pan, even if it isn't perfectly cross and browned - and I would declare the food from your picture perfectly edible.

To set yourself up for success, you should probably not only lower your goals (or lengthen the time horizon until you can cook like a chef) but also give yourself an easier task. Frozen seafood is quite tricky. Seafood in general is fickle, and frozen makes it worse. I would suggest to start with something easy, like freshly cut vegetables, and take it from there. Don't choose something that's too watery (such as mushrooms), or something that won't cook through (such as potatoes). Also it would help if you have a good pan (althogh the tricky part is, as a novice you can't tell when a pan is working well and when it isn't, and you maybe don't have the nerve to care for something like homeseasoned cast iron). It's not that you can't cook in a bad pan, but a good one gives you more leeway.

What also makes your situation different from the chefs is your range and the swirls. As for the range, if you have a gas oven, you are lucky - but it is still less powerful than a professional one. Electricity, including induction, restricts you, and you have to learn to work around that, which makes the learning more complex. As for the swirling, my suggestion is to not learn them at all. They are good if you want to show off in front of a TV camera, or if you are in a hectic professional kitchen for 14-hour shifts, and don't have the time to grab a spatula. At home, it is easier to just stir with an implement and avoid the complexity of learning a motoric subskill at the same time you are learning the main skill.

When you are set to go, all you need is patience and attention. Attention, to make sure you notice what is going on in your pan and how the food is changing. Patience, to repeat it hundreds of times (and also to not intervene when not needed! I knew somebody who was so jittery when around a pan, he had to stir the whole time - his food was always terrible). When you are done learning, you will be able to take a look at a pan and know whether at this moment, the food in it needs stirring, or more heat, or less heat, or more oil, or maybe something else (when you go to more complicated techniques). But it is not something that you will be able to describe in words to another person - it is implicit knowledge you have to train in yourself.

An important element to cooking fish is the quality of the fish itself. Many fish processors use sodium tripolyphosphate (STPP) to preserve the fish. Unfortunately this also makes the fish absorb water. What you end up cooking is a "balloon" filled with water. As soon as the proteins begin shrinking, the excess water is expelled quickly which lowers the temperature of the oil as all of the energy is spent boiling the water that is already outside of the fish.

With the oil at low temperature, the fish will not brown effectively. Additionally a lot of oil will be carried away by the boiling water and scattered outside the pan.

The best way to cook STTP processed fish is to cook it very slowly at a low temperature so that the water content of the fish is not lost completely. You will not be able to brown the exterior, of course.

Or you can buy fresh "dry packed" fish - meaning that the fish has not been treated with STTP and packed dry and not in cold water. Cook this fish in a fairly small amount of relatively hot oil (325-350 F) for a short period of time.

Just before placing the fish into the pan, set the power to the highest setting so that the oil can stay hotter and cook the exterior of the fish faster, making it brown without over cooking/making it chewy. Use butter in the oil and optionally just a bit of baking soda tossed with the fish before cooking to increase the browning effect.

Place it in the pan and let it sear on one side without flipping or tossing. While searing, tilt the pan to collect some of the oil/butter and spoon it over top of the fish until it is ready to turn. Turn over the fish and allow the other side to cook through for 1-2 minutes. You will probably not get good browning on both sides without over-cooking. Such is life in a home kitchen - and even in many pro kitchens.

Don't forget to turn on the exhaust fan and remove the pan from the stovetop immediately when done. The oil will flame up very quickly if you forget and leave it on the burner for a few extra seconds after removing the fish.

Squeeze it. This is frozen seafood. Freezing food creates tiny sharp ice crystals that break a lot of the cell walls, and releases trapped moisture. When you defrost you need to squeeze all that loose moisture out or you'll end up boiling rather than frying. So squeeze the seafood between some paper towels or with a clean dishcloth. Then wash the cloth to get rid of the seafood smell.

Flour it. Burst cell walls is also why it sticks. All those little holes mean there is a more porous surface to stick to the pan. To fix this you should flour the outside of the seafood. This changes the outer surface and can prevent sticking. The flour also helps get crispy brown bits. Seafood on its own doesn't really do that.

Use a LOT of oil. If that still doesn't work then use loads more oil. To the point where it's almost deep frying. Most of the oil will remain in the pan since seafood cooks very quickly. Doubly so if it's in small chunks.

Stir a lot: Sometimes the floured food will stick to the pan at the very start. But if you carefully separate it, then the cooked surface will not stick a second time.

When cooking mixed seafood on pan, I always heat the pan with sunflower oil (can be butter) until it's completely covered with hot oil, and then the cooking must be with high fire for a very short amount of time, you will have to taste one of them - once its edible - it's ready. Don't forget to stir all the time. It's very sensitive food.

As you mentioned, you have some problems with frying in general, so I wil give some points to take into account that apply to frying in general. First I must admit that I don't have much experience frying seafood because I don't like it too much, but frying and sautéing things is one of my favourite ways to prepare food.

• Most of the time, you want whatever you are frying to have room temperature. There are exceptions such as when you are making fried rice. However, especially when you are making meat this is very important. There are two important reasons. First, cold meat will cool your pan, prolonging the time until the meat gets a nice crust while leaking more juice. If the meat leaks too much juice, you might not be able to form a nice crust at all because the meat will be swimming in juice. Leaking juice will also obviously make the meat dry. The second reason is that the cold meat might not cook thoroughly.

• Especially when sautéing you want to make crust very quickly to avoid juices to leak. So crank up the heat. You might want to stir like crazy to make sure the food doesn't stick to the pan and get burned. You can lower the temperature after that to cook the insides more thoroughly. With seafood as soon as you get the crust it's probably done. But if you want steak that is cooked a bit more thoroughly, an option is to quickly form a crust using a pan and then transfer the meat into an oven at relatively low temperature to cook the insides.

• You don't want the meat you put on the pan to be watery. Frozen seafood in particular is going to be very wet after thawing. I suggest to gently dry it with a paper towel.

• From the pictures it seems that you have one of those lightweight pans made of aluminium. These make sautéing more difficult, because they lose the heat quickly when you put food in them. Cast iron cookware is very good in that regard, but it takes some love to keep it functional, but any heavier pan will work, too. The rule of thumb is the heavier the pan is, the more heat it will retain.