It does. If you were marked incorrect, report that the next time you do the exercise. If you wished to be really specific, you may add what will be "falling" at the end of the sentence.
Będzie padać deszcz – It will be raining
Będzie padać śnieg – It will be snowing
Będzie padać grad – It will be hailing
Not really. On one hand "padać' has 11 meanings so in some context that could work. On the other hand context you suggest I would say zaraz spadnie/będzie spadać/przewróci się sound much more probable.
And the sentence does not need any context at all to be understood as It will be snowing/raining.
I just wanted add that "pada deszcz" literally translates to "the rain is falling (down)", so even though the noun comes after verb, it's still the subject of the sentence. That's why "pada" must be 3rd person singular. Hence, "pada koty i psy" is ungrammatical; it must be "padają".
Unfortunately, "padać" is a quite tricky verb, which can have up to a dozen different meanings depending on context. When referring to animals, "padać" can mean "to die", as you can see in this news article:
So, if you wanted to illustrate the imagery (not the literal meaning, of course) of "it's raining cats and dogs", you'd need to use the instrumental case: "pada kotami i psami" (the verb is singular here, because cats and dogs aren't the subject anymore).
If you want to translate the actual meaning, you could also say "leje jak z cebra".
Thanks so much for your very detailed explanation. You have read my mind — yet again! You knew exactly what I was getting at — and you answered my question perfectly!
It's good to know that that the Polish language has many colourful sayings. I used to try out many English expressions on my dad who thought them very funny. Whenever he did me favour, I'd thank him by saying "dziękuję bardzo", his reply would invariably be "nie ma za co", I would then say, "to dziękuję za nic". He thought it rather funny.
Have a great day! :)
Of course "Pada kotami i psami" doesn't mean anything to a person not familiar with the English idiom, you'd just get a surprised "co?" ;)
Fun fact: it's quite likely that your Polish interlocutor will not know what is "ceber" in "Leje jak z cebra", the saying is just so old ;)