The specific criterion for the syntactic construction called reported speech (or indirect speech or indirect reported speech) that is satisfied by the two questions (Did she say if I'll be invited? and Will I be invited, did she say?) is that both contain the reporting verb "say" - either in the matrix clause or in what the CGEL (p1204) calls a "parenthetical, a kind of supplement".
Assuming that John is the asker of the question, he could rephrase it in direct speech as: Did she say: "John will be invited?"
The Oxford Dictionary Of English Grammar, in its entry on reported speech (p361), states: "Reported speech is the same as indirect speech." The ODEG continues: "When we report speech we can use an introductory reporting verb (e.g. say, tell). This is the usual meaning of the term."
In its separate entry on indirect speech the ODEG (p214) states: "The term indirect speech is often used loosely to cover the reporting of thoughts, using an introductory verb of thinking."
The Cambridge Grammar Of English (Carter & McCarthy, p805) extends the scope of indirect speech to include utterances that use a noun phrase:
Speech reports, both direct and indirect, are most commonly made with
reporting clauses containing verbs such as ask, say and tell with a
reported clause. There are also other, more indirect ways in which
people's speech can be reported, by using nouns such as argument,
comment, complaint, observation, remark to refer to someone's words.
- I didn't like his comment that we were spending too much money.
- Their biggest complaint was that the room was too small.
The following extract from Yule's discussion of the topic in Explaining English Grammar is more relevant as an answer to the OP's original question about what can be regarded as reported speech (which was closed for reasons unclear to me).
Yule (p274) focuses on the semantic differences between direct and indirect speech, noting that:
The effect of backshift in tense (in indirect speech) creates a sense
of 'more remote' ... This effect makes the indirect speech forms more
like a narrative account of an event ('telling') and distinct from the
dramatic presentation of the event marked by the direct speech forms
('showing').
Yule goes on to introduce a third category that he calls "Summarized reports", in which there is a even greater remoteness between what was said and what is reported.
The functional distinction between the dramatic nature of direct
speech and the narrative effect of indirect speech is made more
extreme when the structure associated with indirect speech is used to
summarize a speaking event as a way of reporting it. The difference
between what was actually said, as in [8a], and how it was reported,
as in [8b], can be quite large.
- [8] a. "I am waiting here for you. Where are you? You're never on
time!"
- b. He complained about her being late.
The summarized report in [8b] creates an even greater distance between
the speaking event and the reporting event. It also results in much
greater control being taken by the reporter for the interpretation of
the speaking event. There is, then, a conceptual distinction between
the three types of reporting formats in English (Direct Speech,
Indirect Speech, Summarized Report).
Yule differentiates between the words typically used in the three "quotative frames". For direct speech the quotatative frame includes verbs "which indicate the speaker's manner of expression (e.g. cry, exclaim, gasp), voice quality (e.g. mutter, scream, whisper), and type of emotion (e.g. giggle laugh, sob). It can also include adverbs (e.g. angrily, brightly, cautiously).
The quotative frame in indirect speech tends to include verbs "which indicate the purpose of the utterance (e.g. admit, agree,deny,explain, promise, repsond, suggest). Such verbs present an interpretation by the reporter of the speech act being performed.
The quotative frame in summarized reports includes verbs such as "chat, describe, gossip, speak, talk".
Best Answer
There are some clues you can get by studying the form: negative assertion, metaphor, marker phrases etc.
But here's a definition of a rhetorical question from Wikipedia:
I don't mean to repeat what you already know, but this is precisely what rhetorical questions are.
A rhetorical question is built deep into the context and you cannot separate one from the other. You have to be exposed to the message in the context for you to appreciate the rhetorical device.
If you really wanted to, one thing you could try is to answer the question quietly inside your head. If the combination of the rhetorical question and your answer seems silly enough in the overall context of things, then your hunch that it's a rhetorical question is very likely correct.
Ex. It's time to act! If not us, who? If not now, when? What are we waiting for?
Ex. How stupid is this new filing system we have?
Ex. A: Did you get some last night? B: Is the sky blue?