The negation of already in general is not yet.
Sentence 1 sounds wrong, and correct would be
- I haven't cooked dinner yet as the stove is not working.
Sentence 2 is wrong not only because of the use of already, but also because owning ("having") a book continues into the present, hence
- I hope you don't have this book yet; I('ve) just bought it for you.
Or, using a verb that indicates an action completed in the past as intended by the OP:
- I hope you haven't bought this book yet; I('ve) just bought it for you.
However, I can think of rare instances where not already might be warranted:
I hope you haven't already cooked dinner. I brought us some take-out from Trotter's.
(Of course the sentence also works with not yet.)
The reason why I feel it might work here is because the negation is not on the time attribute (already) but on the whole phrase "already cooked dinner". There is a positive expectation in that phrase, which gets negated in its entirety.
I'm not sure this makes sense, so let me give you a similar construction: As a rule, some is used in positive statements, any is used in negation and questions. (E.g.: I eat some pie. There isn't any pie left. Is there any pie left?) However, when we offer someone pie in form of a question, we use some instead of any despite it being a question: "Would you like some pie?" The reason, I have been taught, is that the questioner is implying an affirmative response. So it's more like "Surely you'd like some pie!", as opposed to "You don't want any pie! Do you?"
So in a similar vein, the questioner in the above statement does not want to imply that the (spouse?) has been remiss in cooking dinner and it's not cooked yet. Rather, she's trying to convey a positive message: instead of already cooking dinner we'll have take-out!
Do I find agreement here?