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Honestly, the best way to learn to battle competitively is to build standard team that someone else who's good at Pokemon uses, and literally practice by copying their strategy. You sort of learn the rules of battling more organically that way.

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Question 1: Is this right, is this a good way to start?

Not really. More important things to learn are Pokemon categories and types. Types are literally the most important thing about competitive battles. If you don't have a nearly flawless grasp on type match-ups, you will lose with even the best teams. By battle categories, I mean the role each Pokemon will play on your team. There are Walls, which are meant to be durable Pokemon that can outlast your opponent. These Pokemon usually have high defensive stats but low attacking stats. There are Sweepers, which are meant to be your power houses. They usually have high offensive and speed stats but lower defensive stats. There are a lot more, but in the beginning you want to just focus on these two. Who's good at attacking and who's good at defending. That balance can be key.

Question 2: Attacks have some stats, power and accuracy. Power probably affects damage and accuracy the probability of the attack to hit the enemy But obviously stats like Defense and attack also influence this. Is there some sort of explanation or a formula, to describe more in detail which effect each stat has on the result?

Yes. The damage that an attack does depends on those things and type. The higher the user's offensive stat, the more damage the attack does. Once that's factored in, if the attack you use is the same type as the Pokemon using it, the attack get's a 50% power boost. That's called a Same Type Attack Bonus. (STAB) After that, the higher the opponent's defensive stat, less damage the attack does. Lastly, depending how well or not the opponent's type resists the attack, the over all damage can do as much as 4x the damage or as little as .25 times the damage. The order I think is Base Power - Attack Stat - STAB - Defense Stat - Type Match Up.

Question 3: Some attacks have the type special, I assume this means Special attack and special defense is used to calculate the result, am I right?

Yes. Psysical attacks only incorporate the attack stat of the attacker and the defense stat of the opponent. Special attacks only incorporate the special attack stat of the attacker and the special defense stat of the opponent.

Question 3: Some attacks hit multiple rounds, like uproar. Is the power meant for each of the attacks or for all attacks added together? Same for attacks with multiple hits in one round, like fury attack.

In both cases, the power is meant for each individual attack. That's why attacks that hit multiple rounds are generally more powerful than multiple hit in one round moves.

Question 4: How much should I look after side-effects like poisoning, or should I go simply after max damage and accuracy?

Status effects are really important, but you need to learn more about both the statuses' effects and the types of Pokemon you want to use them on, and the types of Pokemon you want to use them. Burn lowers the physical attack stat of the opponent by 50%, so it's best to use on Pokemon with a high Attack stat. It's best to have a Pokemon with a good enough defensive stat using an attack that inflicts burn. Paralysis lowers the sped stat of the opponent by 50%, so it's best to use it on a Pokemon with a high speed stat. Again, you probably want a Wall inflicting this status. Regular poison is outclassed by every other status and should never be used in competitive play. Badly Poison (Only Toxic and Poison Fang can inflict this status) lowers the opponent's HP more and more longer they are on the field. This is good against sweepers (if burning and paralyzing are inaccessible options) and especially Walls. Walls and really fast Pokemon are usually best for inflicting the badly poison.

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I think the attack-set should be diverse enough, so that I could be effective or at least not inneffective against each of the Pokemon-types. Is this thinking right? After that I should choose Pokemon that canlearn these attacks and hopefully have the same type as the attack, to gain a bonus. I also think I should choose Pokemon with good base stats in the right category, so for moves in category special with high special attack. Is that right? Any other tips to start of developing a good team?

Eh. The golden rule is diversity. Never have two moves of the same type on one Pokemon. It's also good to learn types and type combinations with good coverage like Electric-Ice, Electric-Water, Dark-Fighting. Ground moves have good coverage. Rock moves have good coverage. Ice, Fire, Fighting have good coverage.

The most important thing to do is think of what kind of Pokemon you want to be the focal point of your team. What's it's role. What are it's strengths? What are its weaknesses? Add Pokemon to the team that compliments it's strengths and supplement it's weaknesses.