Honestly, I don’t find this film difficult to understand. It’s not ambiguous, I think it’s quite clear what Bergman is saying. Of course, I may be wrong,
First, you must understand that Elizabeth is the person and Sister Alma is the persona. (* – See comments for explanation of this unclear sentence). There are plenty of indications of this throughout the film, in both content and form.
Elizabeth has an identity, she is an actress with a husband and son. She is quiet and contemplative because she is the external aspect of the person. Alma represents the inner turmoil, the self conflict. Elizabeth is studying her (i.e. the content of the letter), just like anyone experiencing introspection.
Alma screams that she is constantly changing, this is because, while Elizabeth will never change in appearance, her persona is constantly changing. Alma leaving on the bus, right after shots of a film crew, indicate the transitive nature of that persona; Alma leaves, and, like an actress who has finished performing a role, Elizabeth’s persona changes – Alma is no more. Elizabeth is an actress, but it’s indicative of the personality of human beings in general – we are all acting, always fulfilling a role, and, in doing that role, we create a real, definable character of ourselves, through our actions – this is our persona. When our actions are altered our persona is altered; as we change how we act, our persona changes with us.
Sister Alma is called ‘Sister’ Alma because, while the two aspects are actually one, Alma is the subvenient one (Elizabeth, supervenient), a kind of ‘tag a long’, the inner, sister, part of Elizabeth… the ground of Elizabeth’s being. A change in Elizabeth’s character suggests a necessary change in Alma (Elizabeth’s persona), while a change in Alma (Elizabeth’s persona) does not necessitate a phenomenal change in Elizabeth’s character. This is the basis for all of Alma’s conflict, it’s why Elizabeth remains unchanged until the end of the film; we are watching the profound underlying aspect of consciousness, the active inner part that guides and influences our emotions, and that our thoughts are only partially aware of. Elizabeth is only partially aware of what’s going on with Alma – what’s going on within her mind. When Alma gives Elizabeth that speech about truth and being real and honest, it’s because Elizabeth is this facade, this forefront of her identity, the conscious aspect that is only partially aware of the truth of her being. All that is not conscious – her persona – is hidden from her, though it’s trying to make itself known.
In the one scene where Alma is with Elizabeth’s husband, we see Alma, but this is superimposed with foregrounded images of Elizabeth. We’re seeing the persona, but the actual person is Elizabeth. This is why Alma suddenly realizes that it’s her lover, because it really is, and always has been. Since Elizabeth’s husband’s name is left out, it’s likely that the name Alma gives her fiance (can’t remember it at the moment) is actually the name of Elizabeth’s husband. (Seeing as they are two aspects of the same identity). The son that exists, despite the attempts to abort, is Elizabeth’s real son; Alma’s story about having an abortion is Elizabeth’s persona, her conscience, finding a way to hide itself, out of fear, from the truth that she has a son.
Finally, the film speaks in metaphor, this is a function of art. It’s neither necessarily linear, in time, actual, dream, or w/e you want to call it – It’s a film, it should be treated as such. The scenes are there to convey something – an idea, an image, a meaning – and Bergman uses form to do this in the most effective manner. It doesn’t all have to make sense on a literal level, it’s the experience, the stream of consciousness that it imparts, that matters.