1.
In my opinion Kate was a complete brat at the beginning of the play, ultimately this was a result of how her father raised and treated her and Bianca. Because her father chose a favorite child, Bianca, Kate thought she needed to act like a psycho in order to get attention. Then Petruchio comes along, in my opinion he is a somewhat greedy person because he was seeking a wife in order to increase his wealth. When learns of what he will receive if he marries Kate he decides to take on the task of taming Kate. He is probably able to see the source of why she acts like a brat and thinks that it will be a some what small task, considering the reward he will receive. Bianca aka goody two shoes is quite the con artist. She is always sure to say what her father wants to hear and do as her father wants.. She does this in order to remain the favorite. Lucentio is a love struck fool. He is willing to do what ever it takes to win the hand of a women he hardly knows. I think that Shakespeare gave him that personality because, well someone has to be the love struck fool.
2.
I think that Kate's view of marriage was a Christian one because the way that she described marriage was very similar to how the Bible describes marriage.
3.
I think it is rather obvious the Petruchio tamed Kate and did a very good job of it. Based on the way the last scene was depicted in the movie I think the last scene was not a private joke between Petruchio and Kate because Petruchio acted nervous when he sent for Kate.
