"Soooo... Booker is actuallly Comstock right?"
Booker and Comstock are the same person yes.
"and Anna is Elizabeth..."
Yes.
"who is that guy in the begining of the game? The dead one in the lighthouse."
I was always under the impression that he was someone from Columbia or hired by Columbia to keep Booker from boarding the rocket. Evidence for this is a note from "C" (Comstock) on the map in the lighthouse saying something like "He's coming, be ready for him." Also in the Lutece labs there's a picture of the lighthouse with the caption "Only one obstacle" written on it.
"He sold his daughter to Lutece? why?"
Pay off gambling debts.
"was Lutece the one he owed money to?"
Not that we know, at least. We don't know exactly who he owed money to.
"Comstock from another dimension took Anna to his dimension? Why?"
So he could have an heir. Comstock had become infertile due to frequent usage of tears.
"had he sold Anna as well and wanted her back?"
Yep Booker changed his mind and wanted Anna back.
"Maybe he trapped her into the tower to not loose her again.Or was it actually to fulfil his expectations?"
I think it was mainly just to keep her isolated her whole life so that she would be easily indoctrinated and submissive.
"Wtf were the Luteces exactly? Just scientists? Why were they appearing again and again throughout the game?"
They are two alternate versions of the same person from two different universes. In one universe they are male, the other, female. They both discovered the ability to open tears and so naturally, they found each other at that moment. Comstock attempted to kill them using the siphon so he could cover up the whole Anna debacle but he instead just spread them through the probability space and essentially gave them the power to be time and space gods and appear whenever and wherever they wanted.