Re: Uses of 有

你聽日有冇返工？我地今日有冇去邊道？

Wrong position of the verbs! Correct word order should be 你聽日有冇工開？我地今日有冇邊度去？
The verbs 開 and 去 should be placed at the end of the question.

Another question would be if this was true, what are the limitations to its uses?

Seems that there are no limitations to its usage. We can also say 有冇乜野想買? 有冇錢借住畀我先?
Just put the noun immediately behind 有冇.

Another guess I have is that it's actually a "there is/there are" usage, and the following verb functions as a noun.

The verbs (開 and 去) still function as verbs, and the nouns (工 and 邊度) still function as nouns.

你有冇覺得凍啊？你有冇肚餓啊？ - I'm guessing for this one, it's function seems to be to add a hint of concern.

你有冇覺得凍啊？ sounds unnatural. A better version would be 你覺唔覺(得)凍呀？
你有冇肚餓啊？ sounds even more weird. Better versions would be 你餓唔餓呀？你肚唔肚餓啊？你覺唔覺(得)肚餓呀？

You can say 你有冇覺得唔舒服啊？, but it would sound weird to ask 你有冇覺得舒服啊？

The first question sounds okay. The second one should be 你覺得舒服啲嘛？

P.S. - This interesting thread should be moved to the “Practise Cantonese” forum.