Regarding 1 - There is a rule (will add source, later - there are a few) that if one says "I will sin and do teshuva then sin again", the teshuva is ineffective. So, at the least, prior to doing to teshuva, one needs to realize the severity of the sin sufficiently to the point that he resolves not to repeat it. To me, that seems like he definition of "regret".
Regarding 2 - There is no single clear way to do this. Each person's emotions, behavior and thinking is different. One way that I have heard from numerous people is this:
One must imagine God as a benevolent father. (Not so ridiculous esp. when the term Avinu Malkeinu is used so much during the High Holidays!) Your father would do anything whatsoever for you and expects the best behavior from you and loyalty to him in return. If God is your father, and you have sinned, essentially, you have been disloyal to him and disappointed him. You haven't lived up to his standards and his standards for you are placed in a way that is designed to benefit you and improve your life. It's for you; not for him. Wouldn't you think to yourself, "How can I disappoint my father who has been so good and generous to me?"
Such is your relationship with God.
Perhaps, this helps.