Is a "vung" a specific Vietnamese geographical unit, or is it just a general term for zone, region, area, etc.?
It's just a general term like you said, not used very often in everyday speech though, at least not for Southerners.
What is the difference between thấy and xem?
"thấy" is seeing, which is inactive image perception. "xem" is watching, which is active image perception.
Why is "area" marked wrong? And why in other answers, scenery and zone is accepted but is wrong here?
Yes, yes yes. "Region" or "area" are more common usage in this context than 'zone'.
'quan trọng' - easily confused with 'quan trong'.