Translation:It is rainy today.
The kanji for "rainy" looks like a window with rain outside, that'll make it easier to remember ^^
I think you need a different verb conjugation for that present continuous tense. I think it is the te-imasu one.
That, and because the Japanese sentence doesn't have the verb "to rain" in it -- only the adjective "rainy". Note that the sentence ends in です ("is"), not -ます (verbal ending).
Correct! The progressive tense of precipitation would be ふりています (「今日は雨が振りています」 = "Today it is raining"). And yes that verb is indeed missing in this sentence!
Close, but this is wrong: Be careful of the three different verb categories: う ending, る ending, and irregular (like verb+する). Though it looks like a る verb, this is actually an う verb -- not る, so it gets conjugated with って. "It is snowing today. = 今日は雪が降っています。= きょうはゆきがふっています。"
Hmm... I am by no means anything near a native but my hunch would be 「きょうはあめがふりましょう」, take or leave a ね or a よ at the end.
きょう（今日） = today
は = conversational topic marker ("regarding today...")
あめ（雨） = rain
が = helps-with-the-verb marker
ふりましょう（振りましょう） = going to rain / let's rain (change す to しょう)
Well, you can, but that is not what the Japanese sentence is saying. It doesn't have the verb "to rain" in it -- only the adjective "rainy". Note that the sentence ends in です ("is"), not -ます (verbal ending).