i wrote english translation "Do you have question" and it was not aaccepted...why?...
Because it's grammatically incorrect. In both languages you need an indefinite article when something is indefinite and singular, and you don't use one when it's plural. This means that here, it can only be plural "questions" (It will be understood by a Danish speaker as plural in the same way "I have sheep" is understood as plural in English).
The singular sentence "I have a question" would be "Jeg har et spørgsmål"
Den Danske Ordbog (ordnet.dk) gives the etymology as: "gammeldansk spyrjelse, ældre nydansk spørgsel - omdannet i analogi til mål 'tale'." This translates roughly to "Old Danish 'spyrjelse', Early Modern Danish 'spørgsel' - changed in analogy to 'mål' (speech, utterance)." So basically the older form of the word came from the verb 'to ask' (Old Norse spyrja) + the ending -else/-sel which turns it into a noun. Later -sel was replaced by -mål, seemingly due to influence of other words with -mål.
tl;dr - you can essentially look at the word as being made up of 'spørg' (ask) + 'mål' (speech).