Idealism

I see you are at least considering Trotskyism. That's good. You should ask some specific questions about Trotskyism on the trotkyist subforum.

well the public power is the armed bodies of men (police , army). Engels says that as class struggle develops this public power will swallow the state ie. the bourgeois 'democracy' in order to save it. This is how the military dictatorships are created. Also it might be a refference to the wars between big nations.

haha well when something is hard read it again and try to look up hard words in the dictionary :P
But I can always help you. <3

Do you mean this?
"The second distinguishing feature is the establishment of a public power which no longer directly coincides with the population organizing itself as an armed force. This special, public power is necessary because a self-acting armed organization of the population has become impossible since the split into classes.... This public power exists in every state; it consists not merely of armed men but also of material adjuncts, prisons, and institutions of coercion of all kinds, of which gentile [clan] society knew nothing....""
It is self-acting, meaning that it is not controlled by the population as a whole. Indeed the armed bodies of the state are not contolled by the majority but by the minority (bourgeoisie). In a workers state the workers militias which take the place of the army are controlled by the population (working class and peasantry) and they are not self-acting . I hope this clarifies it.

Yeah of course. I reccomend that you buy it as a book because online it's hard to read.
Anyways State and Revolution is a Great book. Don't just go through it when you read it but take time to understand what it says. First time I read it I didn't understand much, but now I enjoy it every time I read it. It's so good!

The vanguard leads the working class in the sense that it is the most class conscious part of the working class, organized in a party.
That's not criticism haha.

Anyways I think it's better to read stuff and observe society rather than being in constant phobia of "authoritarianism"

The party's aim is to inject revolutionary socialist ideas to the working class.
The control of the post-revolution society is under the workers councils, just like in the Soviet Union before degeneration .
Although organized parties still exist, the workers can join whatever party they want.
Don't forget that a party is only a group of people with similar ideas, not a government.

Although I can understand your confusion due to the caricature of the Stalinist Soviet Union.

By consensus
They use consensus in order to take decisions, so if someone doesn't want, then the whole plan fails, just because one person disagrees. So they sit there and debate or force that person to agree haha. That is how democratic some anarchist groups are.

Others are just a bunch of individuals, who do whatever they want . This is not an organization, its a collection of people who cannot make a single collective decision. How can these people lead the proletariat to victory?

Well they don't organize themselves through means of democratic centralism.
Which is a mistake because they become disunited and undemocratic at the end.
Just look how the CNT leadership collaborated with the bourgeoisie in Spain.

Hey you can find a marxist FAQ here:http://www.newyouth.com/content/view/129/63/

I am sure that you can find other FAQs online too, but this is one of the good ones, for beginners to understand the basics. I recommend it