I'm learning Vietnamese with a fluent speaker next to me and they think these sentences are ridiculous.. Duolingo should use sentences that are actually used in real conversations. "cô ấy là bé gái" makes no sense. You refer to an older woman as "cô", but you're calling her a younger girl in that sentence.
The placement of the adverb has an effect on the sense in English. "I am forever in kindergarten" and "I am in kindergarten forever" are not used in the same sense. The former means "I am there all the time" and the latter means "I will never escape." (If you doubt me, try "I really love you" and "Really, I love you" and "I love you, really" on your significant other.)
Prepositions are highly idiomatic in all languages and English is no exception.
For a kindergarten, "in" and "at" both sound normal and common. You could try to make up a distinction but most of the time it wouldn't matter.
For a train station, "in" means inside the building, but not all stations have a building. Some just have a platform. "At" is a bit more vague and could include inside the building but also waiting in a car parked in front of the station, etc.
In English "kindergarten" can refer either to the class of children, the educational level, or the place where the education is conducted. The place can be a classroom or anywhere the class normally is held. The use, or non-use, of definite articles depends the speaker's conception of the sense of the word. If he means it as a particular, known, kindergarten he will say "the kindergarten." If he means it as one kindergarten out all kindergartens he will say "a kindergarten." If he means it as the designation of educational level he will say " kindergarten" with no article. All are correct and idiomatic but are different in sense.