Generally, yes. He regrets the murder immediately after doing it. "Wake Duncan with thy knocking! I would thou couldst."
Macbeth pretends to mourn for Duncan's death to maintain his facade of innocence and loyalty. In reality, Macbeth is motivated by his ambition and desire for power, making his grief insincere.
She didn't want to kill him herself, because she said Duncan looked like her dad while he slept. She did have Macbeth murder Duncan nonetheless
why was macbeth releuctant to kill duncan
No, King Duncan hugged Banquo, because he says "Let me enfold thee in my arms" to Banquo. But it's really up to the director if he or she wants Macbeth to hug Duncan also.
Duncan plans to spend the night at a hotel nearby.
"I" said Macbeth, "with the servants' daggers. I killed Macbeth."
He claims he did so out of anger over Duncan's death, but it is really to prevent them from telling the truth.
Duncan's trust of Macbeth shows he is a bad judge of character. The fact that he is willing to stay in Macbeth's home and ultimately dies for it is because of his inability to recognize who Macbeth really is.
Macbeth believes he has to kill Duncan's guards in case they heard anything happen in the room while Macbeth was killing Duncan.
No. King Duncan was clueless. He admits it himself: "There's no art to find the mind's construction in the face; he was a gentleman in whom I built an absolute trust." He had no idea what was going on with Macbeth. Macbeth really expected to be named as Duncan's heir (he was after all a successful warrior unlike the feckless Malcolm) and was shocked and hurt when Duncan named Malcolm Prince of Cumberland. And then Duncan says "And now the party's at Macbeth's place!" He was, as I said, clueless.
Duncan and Macbeth are cousins. Therefore, they are bound by kinship. They are also bound by subject and host, as Macbeth is hosting Duncan as his guest.
Macbeth was not a vassal of King Duncan. Macbeth's act of killing King Duncan would be considered regicide because he unlawfully killed his king, who was his sovereign and ruler.
Macbeth kills Duncan's grooms after Macduff discovers the body.