Whose grandfather? It is understood to be "my grandfather ". Otherwise, the sentence does not make sense.
Then, "This watch is for my grandfather" should be considered correct.
Not necessarily. As an example - A mother could easily say this sentence to her child. In this case it would imply 'your grandfather'. So no, we cannot assume the relationships in this sentence.
Which case is dziadka here?
Genitive, as needed by 'dla'.
jestem w domu is also locative isn't it? Sorry for different example but I missed to ask in the right one. By the way shouldn't the genitive be dziadki?
"jestem w domu" takes Locative indeed.
No, 'dziadki' is how the Genitive would look like if this word was feminine and its basic form was "dziadka". But it's "dziadek" in Nominative, so "dziadka" in Genitive.
Of course! Thanks again!