This is an extraordinary scene in which Juliet goes from the warm contentment of her wedding bed, to the sorrow of a (temporary) parting from her love, to utter despair. She wakes knowing Romeo has to leave (she even tries to wish it away)but hopes- perhaps even expects- that she will be reunited with Romeo according to the Friar’s plan. She manages to very cleverly deflect her mother’s inquiries about her weeping. Read Juliet’s responses starting around line 73 carefully and ask if her mother and the audience comprehend her responses in the same way. Soon, she is given the news she must marry Paris. Her reaction is understandable to the audience; less so to her parents.
What follows is scene to which an audience member can only react with horror. Capulet is irritated by Juliet’s lack of obedience and his initial expression of irritation soon grows to a towering rage when Juliet refuses to yield to his will. In lines 147-157, 160-168, and 176-196 Capulet “is too hot” and heaps insults on his daughter, basically calling her a whore and condemning her to a life of street prostitution if she doesn’t marry Paris. A father saying such things to his daughter surely must be designed to leave an audience sympathetic towards Juliet.
As if this is not bad enough, when Juliet seeks help from her mother, Lady Capulet callously says she is done with Juliet. Juliet turns to the one person from whom she can expect solace, her surrogate mother, the Nurse. She receives none and is left with no one to turn to, except the Friar. Juliet has now been placed in an impossible position; she is married, possibly pregnant, has a banished husband and is expected to marry another man or be disowned. It would be a hardhearted audience member indeed who was not sympathetic.

I have a somewhat different take on the subject. I presented a paper on the popular perception of R&J at a Shakespeare conference last year. My argument is that the whole notion of age of consent and the shift towards "love matches" (rather than those of parents) is being questioned by Shakespeare. In 3.5, Capulet is raging and it is easy to side with Juliet in her choice to marry Romeo rather than Paris. But conversely, we see that Juliet is not much capable of making her own decisions. She is too young, too inexperienced, and too immature to make this crucial life (in her case, death) choice.

I am not saying that Shakespeare condones the elder Capulet's behavior, but he and his audiences were exploring the ramifications of this relatively new way of chosing a marriage partner.

Many of the questions you've asked are to be answered in your own opinion. Try to picture yourself as a kind of family counselor. Is the stern approach to parenting taken by Juliet's father an effective way to make his daughter obey his commands, or do you think...