Am I imagining it, or is there a bit of an "s" sound before the "t" in the pronunciation of "vårt"?
It sounds to me like "voist" when you hover over the word in isolation but not when you play the whole sentence.
Why doesn't fit the "this" word at the beginning of the sentence if I can read "it is our glass." is fit? Like that: "This is our glass"
"Det er vårt glass" = "[It/That] is our glass"
"Dette er vårt glass" = "This is our glass"
"That's our glass", is not among the correct solutions.
Sometimes vår comes before, and sometimes agree the word. How does one wow which is the way to go? Ex: Det er vårt glass Jeg liker hesten vår(one of the questions)
The possessive can go before an indefinite noun, but it must come after a definite noun. "vårt glass" (possessive adjective "our glass") or "glasset vårt" (possessive pronoun, kind of like "the glass of ours" except that in Norwegian this has more the meaning of "the glass which happens to be ours" The emphasis is less on the possession and this is the more common form.) http://grammatikk.com/pdf/Possessiv.pdf
There's a slight difference in that "vårt glass" would emphasize the ownership the glass, while "glasset vårt" wouldn't. "It's our glass" vs "It's our glass". Both are perfectly acceptable, but "glasset vårt" is definitively more common.
In Russian, it's other way around. Is the indefinite form more appropriately used in poetry, as it is in Russian?
Yes. "Det er vårt glass" emphasizes who own the glass, while "Det er glasset vårt" would be used in normal conversation. Both are grammatically correct.
et glass = neuter gender = vårt
-> Det er vårt glass.
en hund = masculine gender = vår
ei bok = feminine gender = vår
-> Vi elsker hunden vår.
-> Vi leser boka vår.
katter = plural = våre
-> Kattene våre spiser mus.