When a narrator filters the thoughts of characters, can the narrator ask a question as if it comes from him or her?
For example:
“Who could ask such a question? John was upset.”
Or
“Was she scared? Carrie went to the hospital.”
Could these kind of questions be interpreted as direct thoughts?
It's useful to think of the narrator as an extra character for a moment - yes, even when ze's a featureless ghost (as is often the case).
Why does ze ask a question in the narration?
Does ze not know the answer and is wondering zirself?
Is ze teasing the reader - knows the answer, but won't reveal it just yet?
Is it a rhetorical question?
Next step is to figure out if the reason for asking the question is consistent with the narrator's characterisation.
If the narrator doesn't know, is it consistent with the amount of information ze's established to have about what's going on?
If ze is teasing the reader, is it consistent with zir personality - and does ze even have enough of a personality for that?
If it's a mere rhetorical question, is this consistent with the style in which the narrator expresses zirself throughout the text?
If you answer "yes", then there's no problem. If you answer "no", then asking a question would be a bit of an out of character moment.
P. S. After seeing this question, I'd like to clarify that what I said above applies when it's the narrator who's asking (like you stated at the start of the question). If ze reproduces a character's inner monologue in semidirect speech, then it's the character asking themself a question, not the narrator.
In your examples, I would interpret both as an indirect representation of that character’s thoughts. That their thoughts could be summed up in those questions. Virginia Wolfe used this POV in “Mrs Dalloway,” and its filled with these kinds of character thoughts.
If you want your narrator to be sharing their own thoughts, in addition to character thoughts, then keep in mind the emotional distance in the scene. For instance, if the narrator is sharing a character’s inner most self, then emotions will seem like they belong to the character in the frame.
To make it clear that these questions are coming from the narrator, widen the emotional distance scene. By that I mean don’t talk about the character’s experience and focus on the setting or some vantage point that the character could have. A silly example would be to talk about the weather in Tibet a hundred years ago. The idea is to shift the readers focus from the character’s voice to the narrative voice. Then, the narrator can talk about anything they chose to talk about.
A way to imagine it is like in a movie. Some shots are close in and really show the character well, then the shot pans out and pulls back revealing more of the world.
As they stand, your examples are ambiguous and confusing to the reader. Who is asking those questions? Your examples can be interpreted in several ways:
The narrator is asking:
Carrie went to the hospital. Was she scared? Perhaps. We will never know.
The character is asking herself:
Carrie went to the hospital. She didn't know how she felt. Was she scared? Happy to find help? Her feelings were mixed and confused.
You need to clarify who is asking the question.
In your examples the ambiguity is a result from your syntax. You pose a question, then introduce a subject (John, Carrie). Commonly, when a subject is named, it means that the subject has shifted, for example like this:
John looked at her. Was she scared? Carrie went to the hospital.
In this example John wonders whether Carrie is afraid and watches as she goes to the hospital. If Carrie had been the paragraph's subject before the question, her name wouldn't be repeated:
Carrie looked at herself in the mirror. Was she scared? She went to the hosptial.
But even then there is a kind of non sequitur between the question and the action. There seems to be no relation between asking herself if she is scared and starting to go to the hospital. Does she leave the question unanswered? What does that mean for her? Why does she suddenly get up and go? You need some kind of transition from the question to the action, for example like this:
Carrie looked at herself in the mirror. Was she scared? She turned and went to the hosptial.
Now the one action (looking in the mirror) transitions into the other (going to the hospital) more fluently.
