Hamlet lost the love of his father, mother, and Ophelia. Why is Hamlet responsible for this?in Hamlet

I edited your question down to just the first part because
you are only allowed to ask one question at a time.

In
response to your question I would argue that Hamlet didn't lose the
love of any of those three characters. They were steady in their love for Hamlet until
the moment each of them died.  Hamlet's father was murdered by Claudius; Gertrude
accidently drank poison that was intended for Hamlet; Ophelia committed suicide as a
result of the deep despair over the death of her father and the state of her
relationship with Hamlet.  All of these characters deeply loved Hamlet -- there is NO
evidence to the contrary on that.

Your question asked about
Hamlet's responsibility in these losses.  Again, I would say that Hamlet's
responsibility is limited, especially in the case of his mother and father.  Hamlet has
absolutely NO culpability in loss of his father.  Gertrude's death happens because
Claudius is trying to kill Hamlet.  I guess you could say that Hamlet's revealing that
he knew about Claudius's murder of King Hamlet and his subsequent killing of Polonius
brought on the end of the play with Laertes seeking vengeance and Claudius wanting to
silence him, but that is kind of a stretch to then say that therefore, Hamlet is
responsible for his mother's death.  It could even be suggested that Gertrude drank the
poison as a direct defiance of Claudius and that she was attempting to save Hamlet from
drinking it.

The only character Hamlet is really in any
directly way responsible for is Ophelia.  Hamlet puts on his crazy act with Ophelia,
leaving her very confused about the state of their relationship.  When he realizes that
she is being used by her father, he is rude and condemning of her, commanding "get thee
to a nunnery!"  She is heartbroken and confused when he is flirts with her during the
play-within-a-play scene.  When she finds out that her father is dead and that Hamlet is
the killer, she loses her mind and drowns herself in the stream.  Hamlet not being
truthful with her from the start could be considered a cause of her death, and he is
somewhat responsible for losing her.