"Do you have a girlfriend?"
Maybe if you think of は as having a nuance of "as for X" with the word before は being the X, it might help. が puts the emphasis on what comes before it whereas は emphasises what comes after, so "As for X, this is the point of what I want to say/ask." That's why が comes after interrogative (question) words, the point of your question is to ask "who", "where", etc..
This is the problem with teaching Japanese in this manner. There are no contextual clues. The expression in question is contextually 「(あなたは）彼女はいますか？」or 'Do you have a girl?'. Since the 'you' is only implied the above question could be read as 'Is she present?' 「かのじょは（へやに）いますか？」would be 'Is she in the room?'.
Just to make things more convoluted: 「（あなたの）かのじょは（へやに）いますか？」Would be 'Is your girlfriend in the room?' So, the word かのじょ can mean either 'she' or 'girlfriend'.
So, obviously there are many different possible meanings to any simplified expression. What is discouraging is the fact that the team behind this surely knows this to be true...
In Japanese we usually avoid the use of the words "he/she" casually. In VERY occasional cases you can hear it, but you would almost listen to something in those lines "あの人、私の彼女ではありません。" That person is not my girlfriend "Xさん、私の彼女ではありません" Mrs. X is not my girlfriend.
Also, 私/僕の彼女 is "my girlfriend" in most contexts.
Besides that, only context will say for sure what you mean by 彼女.