Translation:It was sunny yesterday.
This needs to accept "clear" as well, as 晴れ and "sunny" are not the same, but when it's 晴れ(clear), it's often sunny.
You are 100% right. While the skies being clear does imply that it was sunny 晴れ does not mean sunny and that should not even be an acceptable answer.
Unfortunately not. The word 'day' （一日）is not included (except in the word 'yesterday').
Addendum: Full sentence, including 'day':
From my understanding the proper word for "bright" is 明るい。Not sure if this can be used for weather.
There happens to be two は in a row, which is how you write 母 ("mother") in hiragana. In this case, however, the first is the particle は (pronounced wa) and the second belongs to はれ (hiragana for 晴れ, "clear weather" or, as Duolingo says, "sunny"). Normally, of course, the latter would be written with kanji, so the algorithm that supplies the hints doesn't expect this combination.
No. 晴れませんでした/晴れなかった means 'did not clear up'. 'Was not clear' would be 晴れていませんでした/晴れていなかった. 晴れではありませんでした/晴れじゃなかった means 'Was not (a) clear (day)'. 晴れ is a noun. 晴れる is a verb.
All of the above are negatives though. The sentence in question does not ask for the negative.
While the English uses 'sunny' (an adjective), the Japanese noun 晴れ still fits best.