My advisor is planning to take a one-year leave for personal reasons. He will be returning to his home country, and the leave will be without pay. I am currently in my second year as a Ph.D. student. Is it very difficult for me to switch advisors at this point, considering we have already worked together for over a year and everything has been going well? He plans to take leave while still advising me remotely. Does the administration allow this?
Rules vary, but I would expect it to be possible in many(most?) cases. The professor is still a professor at the institution and their employment doesn't end.
They may not get paid for advising you but professors often do a lot without thinking about being paid for individual tasks.
There might be exceptions and it might be hard on you, but I expect it to be allowed.
For a specific answer, you need to ask your institution.