Gusts of wind might be memorable/ distinct enough from eachother in someone's mind that a speaker can refer to them as countable "winds", and weather reporters frequently do (probably in an effort to be extra correct: every gust is different speed, different direction, different time...). But a speaker can also choose not to distinguish between specific instances of wind, and usually when someone wants to refer to a specific gust they will use the word "gust". Note too that less intense/memorable "breeze" and "air" are rarely used in the plural.
ex. There was a strong south wind
ex. There was constant wind and rain
ex. It's a steady wind
ex. Just a light breeze today
ex. There's a foul air around here
It's a matter of perspective, unless someone unconciously talks like they hear on the news all the time (http://schoolvideonews.com/Broadcast-Journalism/Cliches-Redundancies-and-Euphemisms-Part-2)
"There was very strong wind yesterday" is not good English idiom. "There were very strong winds yesterday" is the correct idiom.
Whether that kind of free translation is permitted by Duo is a separate question. If it's based on getting the best and most accurate idiomatic translation, then the plural version is the one to use as the primary translation.
"There was very strong wind " didn't seem quite natural to me (British English), but if googled gives results. Suggested main translation "It was very windy yesterday ". Other possibilities It was really windy There was a very strong wind There were very strong winds There was a very high wind There were very high winds
Because ветер is masculine, not neuter. Ветер is either the subject of the sentence or a predicate nominative - in either position, it determines the type verb to use in Russian. It's like saying "Very strong winds were [here????] yesterday."
English often uses the "dummy" subjects "it" or "there" + [to be] to express an idea which is difficult to state directly.
Dummy-subject: "There were strong winds yesterday"
Actual-subject: "Strong winds were yesterday." That's a really awkward sentence. The dummy-subject is much better.
There's is a contraction for there is. This sentence speaks of the past tense. While I personally attest that certain regions will say, There'us when meaning There was, it's pretty lazy of us. ;) Me. Lazy of me. I never write that, though. But to the point - "there's" would not be correct for this translation.