> 2. How have your research visits usually been funded? Is it the lab the student is affiliated with that generally covers expenses? By how much?

I'm not sure about France/Netherlands, but I think most of the times it's a case by case decision. Sometimes the guess university has a grant to sent students, sometimes the host university has a grant to revive students, sometime both have a cooperation agreement, sometimes it's more weird.

Does the host university have a faculty housing office? You might have luck rending a faculty members flat who is themselves on sabbatical in the fall.