Some specific answers...
E.g. can number of unique cards/characters/doms be multiples within same deck?
In booster the uniqueness rules are turned off in deck building but remains in effect for play. So, you could have multiple copies of a single unique character in your deck, but you can only have one in play at a time.
And after drafting all the cards of all the boosters do the decks have to consist of all of the drafted cards?
No. After drafting all of the cards players have a set amount of time to whittle their decks down to whatever size they can legally make.
Regarding Lost Souls: Let's say drafting contained 6 boosters each having 15 cards in while 4 players are drafting => will all of them have to play with a 90 card deck then + filled up with remaining Lost Souls to get to the appropriate minimun soul number?
No. In booster you start with 8 non-SA lost souls, and any souls you draft can be added to the pool. Once you have all your cards drafted you can build any legal deck from the cards you have. In Lackey there is a special pack of "Booster Draft Souls," which contain the 8 non-SA souls you need for the start. Each player gets one of these packs and it is not drafted.
Lots of questions and still some more. Can this be crosschecked somewhere (i.e. are there written rules)?
Would be great if you could help me out in enlightening and understanding that format more detailed!
Post if you have any additional questions. Even if everyone else it at Nats, I will make sure I look for questions.