"The weather now is dry and also cool."
Nowhere in this sentence did you put the word "very". And then the Chinese translation is expected to have it?
When an adjective is used as a verb, it can't stand on its own under normal circumastances. You have to add a so-called "adverb of degree" (very, really, quite etc.). 很 is the weakest of these, it only really corresponds to English "very" when it's especially emphasised. Otherwise it's more of a placeholder and should not be translated to English at all.
You need to tell when it is normal to use an adjective as a verb (linguists call it a “predicative adjective”, i.e. “to be adj.”).
We can definitely say “现在的天气干燥，也凉快。” unless it would break the rhythm of your speaking. This course just doesn't seem to have intention of teaching this sentence structure. Otherwise in another question we can say “我觉得我的翻译对” instead of the rather colloquial sentence “我觉得我的翻译是对的”.
我很好 =/= very good 我非常好= Very good You basically have to live with this rule.
I understand 非常 to have the meaning of "to an extraordinary or exceptional degree". I think to a degree stronger than that expressed by 很.