I guess in this context "что" is extremely close to interrogative particle.
In Polish, as well as in Ukrainian there exists czy
(чи
), that interrogative particle is used in yes-no questions. For example, phrase, provided in above-mentioned link "Czy ten pan jest z Anglii?", can be translated "Этот господин из Англии" as well as it can be translated "Этот господин [он] что, из Англии"? Also, this can be translated with another interrogative particle, ли
:
"Этот господин из Англии ли"?
Let's look close to your examples, actually, all of them can be replaced by following forms:
- Ты с ума сошёл что ли?
- Я дура что ли?
- Он сам не может справиться что ли? (Or - он, что ли, сам не может справиться?)
Что ли
is, by the way, yet another form of interrogative particle.
It's just that in Russian this form with "что" is definitely have some stylistical connotations. Compare:
"Хочешь булочку?"
and
"Ты что, хочешь булочку"?
In second case one who asks this question is assuming that the answer most probably will be affirmative. Also, such "что"-questions is a bit pathetical ("Мы что же это, Родину предадим?").
As for punctuation, stick with comma after "что", but keep in mind that in some cases when you want to separate second part more clearly, you can use dash as well. In some phrases, especially short ones, you can omit comma at all, no one will judge you hard. By doing this you can convey liveliness of colloquial speech.
xom
(sorry, I have not armenian letters here): 'Xom du gizh ches' :)))