Скоро лето was "It will soon be summer" two questions ago, without будет, and now you have to use будет? Consistency of translations is needed, because another question that omitted будет, rightfully so, was скоро зима for "It is winter soon." The flipping of present and future needs better instruction, Especially because this sentence seems correct compared to the summer question.
It's a matter of English idiom. Mainly, you haven't said what (or where) Spring will be; usual English idiom is: "Spring will be here soon." ("Soon" is an adverb - it describes when Spring will be, but not where or what it will be.)
I can't determine whether Duo accepts "Spring will be here soon" - it is further removed from the Russian than "It will be Spring soon" - but I think Duo should accept it, since the two are equivalent in English.
As a minor second point, English usually refers to the the seasons by themselves without using articles, so usually "Spring is/will be", not "The Spring..." However, it's not incorrect and not extremely unnatural to say "The Spring is...", so I do'n't think Duo should mark you wrong for using the definite article.
If you're talking about a particular summer, then the article is OK: "A summer to remember..."
весна is nominative case. "Spring" is either the subject of the sentence ("Spring is....) or a predicate ("It is Spring"), both nominative case in Russian and in English.
весне is either dative or prepositional case. Dative is usually reserved for indirect objects (which "Spring" is not), and you need a preposition for prepositional case, which isn't present in the Russian sentence.