What is the difference between: ξάδερφος and ξάδελφος?
No difference, just different spellings.
I assume, as with the above example, εξάδελφος can also be used interchangeably? (It's more old fashioned maybe?)
It sounds old-fashioned and is used mostly for fun among natives.
γιατρός -- pronounced like "yiatros" or "giatros"?
Why can't we use προσωπικός for "private" here?
προσωπικός is better for "personal"