Finland is certainly ett fint land ('a nice country') but the name is not because of that, but because Finns live there. The spelling is because we tend to avoid having double consonants before another consonant (this is not a 100% rule though but I'm not going into that right now).
Well... Yes, but sometimes they can be used interchangeably. "Space" implies land with few/no major buildings on it or a large room for a particular event (when used in a context like this). I don't know the connotations of "plat," but it sounds like the English "plot" which would mean the physical land, usually with no buildings. I don't know how it is in Swedish though... Please elaborate?
plats is a cognate of place and has the same meaning, it refers to a specific area – this definition is pretty good: a particular position, point, or area in space; a location (Google's definition of 'place').
space would usually be utrymme or område. Sometimes, especially in American English I think, people use space to mean what we would call en lokal in Swedish.
plats has nothing to do with plot, which is usually jordbit, jordlott etc etc.
"Fin" is not as strong as "vacker", it's a bit like the difference between "pretty" and "beautiful" in English. It's a bit harder to give a succinct explanation for "snygg" vs. "vacker" because I think there's a bit of overlap, but I would say "snygg" has a bit "rougher" connotations, while "vacker" is more along the lines of elegant. Kind of like the difference between "good-looking" and "beautiful" in English. So you have a "snygg bil", a nice, sleek, brand-new red car, and you have a "vackert hus", a house with some beautiful, probably old-fashioned architecture. A woman who is "snygg" might be a bit provocative and fierce, while a woman who is "vacker" might have a more elegant, feminine kind of beauty. Of course, you can also say that "snygg" is just a more informal way of saying "beautiful". Like I said, there's quite a bit of overlap so there are no easy one-to-one translations here.