In Act 1, how does Duncan view Macbeth's actions?
In Act I, King Duncan sees Macbeth as a loyal soldier and countryman. He hears that Macbeth has effectively killed the treacherous MacDonwald. The sergeant enters and tells the king about the brave actions of Macbeth.
For brave Macbeth—well he deserves that name—
Disdaining fortune, with his brandish'd steel,
Which smoked with bloody execution,
Like valor's minion carved out his passage
Till he faced the slave
Which ne'er shook hands, nor bade farewell to him,
Till he unseam'd him from the nave to the chaps,
And fix'd his head upon our battlements.
In order to reward Macbeth for his brave deeds, King Duncan bestows the title Thane of Cawdor on him. This action shows that the king is grateful for his actions and trusts him immensely.
This foreshadows future events. Macbeth has killed one traitor, but he himself will soon plan to kill the king and eventually become a traitor himself. This shows Duncan, who once trusted MacDonwald, has problems picking men of strong morals to trust.
To answer this question, take a look at Act I, Scene II. In this scene, the Captain talks about Macbeth's actions on the battlefield and King Duncan is overcome with pride and gratitude:
O valiant cousin! Worthy gentleman.
Later in this scene, King Duncan pronounces Macbeth the new Thane of Cawdor and, in doing so, refers to him as "noble."
It is clear, then, that Duncan views Macbeth's actions in very positive terms. He respects his military prowess, his courage, and his loyalty. Moreover, he wants to reward this behavior because he knows that it is worthy of merit. In addition, Duncan clearly values loyalty in the wake of the former Thane of Cawdor's rebellion against him.
It is rather ironic, then, that a short time later, Macbeth receives the prophecies from the witches and then rewards Duncan's gratitude by plotting his murder. But this is what makes Macbeth's rebellion so successful: it is completely unexpected that such a loyal servant of the crown should want to take it for himself.