In general, yes-no questions have to start with a finite auxiliary (verb). Past participles and gerunds don't work because these are non-finite forms.
I found a short presentation on auxiliaries on Geoff Pullum's website that might be useful reading: http://www.lel.ed.ac.uk/~gpullum/grammar/aux_sli.pdf Pullum says auxiliaries are verbs that are distinguished from lexical verbs by the "NICE" properties:
- special Negation (precede the negative word "not" or take the negative suffix "-n't")
- Initial position in Independent polar Interrogatives (polar interrogatives are yes-no questions)
- Code interpretation of Complement omission
- special Emphasis forms
Note that this definition doesn't require an auxiliary to associate with any other verb, despite the common grammar-school definition of auxiliaries as "helping verbs". The verb "be" is considered to be an auxiliary by this definition even when it is the only verb in a clause, as in "The rose is red" or "This is a rock." (For more elaboration of the argument for this, see "The Two be's of English", Thomas E. Payne)
Here is a list of the main English finite auxiliary verbs, adapted from Wikipedia:
- do, does, did (can also be a lexical verb)
- am, are, is, was, were
- have, has, had (can also be a lexical verb)
- modal auxiliaries: will, would, shall, should, can, could, may, might
The ones listed above are kind of the most ordinary auxiliaries.
This is definitely an auxiliary, but it can behave a bit oddly since it doesn't distinguish tense like the others. This isn't really relevant to question-formation though.
This is definitely an auxiliary verb in standard English, as shown by how it is negated ("I ought not" rather than *"I don't ought"), and it behaves like a modal auxiliary in particular in its lack of inflection for person and its defective conjugation (no non-finite forms). However, it's a bit unusual as it associates with a to-infinitive rather than a bare infinitive.
I don't think questions starting with "ought", such as "Ought he to have gone?" are generally felt to be ungrammatical in modern English. But I agree that they seem to sound more old-fashioned than the corresponding sentences in the indicative, which is interesting. (Relevant ELL question: Using “ought” in a question: “Ought I celebrate?” or “Do I ought to celebrate?”)
I don't know the reason for that, but it might be because the "to" in "ought to" is closely bound to the preceding word (it's usually articulated as a single phonological word) and fronting "ought" in a question breaks that apart. (Pullum's presentation argues that in the similar expression "have to/has to/had to", the verb "have/has/had" is not an auxiliary at all for most contemporary speakers.)
The fact that, as mentioned in StoneyB's answer to the linked ELL question, the "to" can often be omitted in questions with "ought" might be another sign that speakers think of "ought to" as a fixed phrase, not as the verb "ought" followed by a separate word "to" followed by an infinitive.
This explanation would predict that the negative "ought not to" should also be perceived as more formal than "ought to", and I think that is the case. (theUg's answer to the linked question mentions that some regional dialects form alternate negative forms like "don't ought to" and "haven't ought to".)
- dare, need (both can also be lexical verbs, and often are)
"Dare" and "need" are only marginally used as auxiliaries, and there is a lot of variation in usage. (A relevant web page: The Auxiliary Verbs "Must", "Need" and "Dare") I don't think there is anything special about questions that makes them less suited to be used in this context. Sentences like "Dare he eat that?" and "Need I go?" actually sound better than the corresponding indicative sentences *"He dare(s) eat that" and ?"I need go".