Hi,
Sometimes there can be some confusion between the two kinds of family that you discuss below.
What you say tends to depend on who you are talking to, and on the context.
We usually don't ask a child these things, as we assume they are part of a family.
Do you have a family? Often means 'Are you marriedz? Do you have children?' But if I know you are married, it would just mean 'Do you have children?'
Do you have family? Everybody has family somewhere, maybe alive, maybe dead. So, we usually say 'Do you have family in Montreal?' 'Do you have family here?' etc. We are referring to the larger definition of family, eg uncles/aunts etc. Ths is often called the 'extended family'.
When you ask someone whether he/she has a family or not, which of the above is correct to use? Considering "family" could be:
1. family that hi/she's born in, with a mother and father, brothers and sisters
2. family of his/her own, with a husband[wife] and kids of his/her own if any
Also,
I have no family.
Can this be used for both types of families mention here? Yes. The context usually makes it clear what kind of family you mean.
But you'd typically say it another way, eg 'I have no children'. eg I'm not married'. eg 'I live alone'. eg 'My parents are dead'.
Best wishes, Clive