"Does he have a mother?"
Translation:У него есть мама?
No. It is even stressed in this question.
When you ask whether someone has something, you have to use "есть". У тебя есть ручка? Do you have a pen?
If you say "У тебя ручка?", stressing the word "ручка", you will actually ask if you have a pen - and not something else. As if all the people in the room had pencils and this person had a pen. Like "Is it a pen you have?"
Hope this makes sense. "У тебя мама?" sounds really weird for a Russian ear. I can't think of a context to say so.