Could this also mean "Your questions, please" and "Their questions, please" ?
I believe so since it is at the start of a sentence (and therefor capitalization blurs if it should be her/their/its or your). If there was a sentence before this one that put it in context it would make the definition clearer.
You're right. But you would usually put a comma between Fragen and bitte, like in the english sentence, in my humble opinion.
"Their questions, please" and "Her questions, please." are also possible but less likely. The speaker addresses someone who would be requested to tell someone else's questions.
That seems like a more natural inquiry. People don't often ask someone to provide a third party's questions.
If you are in a group, such as teenpact, and you are interviewing a politician, and said politician dodges a question, you want to ask for that question to be answered. So this sentence could be very useful in a group interview.