"How long do you have?" -- What does that mean?
The conversation regards my potential trip to another country to visit someone.
It means how long I want to stay there? Or How many time I (will) have to stay there?
This asks how much time you have available. It's usually asked in the context of trying to schedule an activity, to determine how long it could be and fit into your availability. It might be part of an exchange like:
How long will the meeting be?
How long do you have?
The implication is that the meeting will be as long as the person can stay.
I think it's more idiomatic to ask
How much time do you have?
In the context of a trip you're planning, it might refer to how much time you have free in your schedule.