How does the director of the 1995 movie Sense and Sensibility use film techniques to explore the theme of betrayal?

Because space is too limited to enable a discussion of all three themes, I had to shorten your question to just one theme.

One technique used to show Edward's emotional betrayal of Elinor is framing. At Norland, when Edward makes a sorry attempt to tell Elinor about his engagement, the scene is framed by the stables. Specifically, when Elinor says the line "Your education?" the lines of the stable that are framing her are vertical, horizontal, and diagonal. Vertical lines in framing show that the characters will soon be experiencing trouble; the situation is "closed" with no way out. The vertical lines behind Elinor are the largest, the thickest, and the heaviest of all the lines, foreshadowing for us that her feelings for Edward are about to be betrayed, or disappointed, by Edward's actions. However, the stables are also composed of horizontal lines, and you can see one diagonal line just behind her. The horizontal lines foreshadow that her problems will be resolved, while the diagonal shows that there will be a difficult and emotional progression leading to her resolution. This is confirmed by the round globes on top of the vertical posts.

The techniques of framing and lighting are also used to introduce us to Willoughby, again foreshadowing that he will soon betray Marianne. When we first see Willoughby on the downs after Marianne has fallen, we see his horse rear. The action shows aggression, but the diagonal line made by the horse also foreshadows that there will be difficult and emotional trouble ahead but that it will be resolved for Marianne. The lighting is significant. Willoughby is introduced in complete shadow, showing us that he is a completely untrustworthy character, despite appearances.

A final technique used to portray Willoughby's betrayal of Marianne takes place at the ball in London. After Marianne cries out "Willoughby!," as she rushes to him, we are given a high extreme long shot of the entire ballroom and all the people in it that are, not only turning to state at Marianne, but also separating Marianne from Willoughby. This distancing long shot signifies that Marianne will absolutely never be joined with Willoughby, due to his betrayal.