"Мені сумно, якщо іде дощ" is as strange in Ukrainian as "I am sad if it rains". To convey the idea that rain makes one feel sad, we would say "Мені сумно, коли іде дощ" -> "I'm sad when it's raining", exactly the same.
I don't like this sentence because it's very unnatural. It's not possible to edit the Ukrainian sentences, only to remove or disable them and create new ones. I don't have access to disable or remove sentences. So we'll just have to live with what we have :/ I'll make a list of stupid sentences and ask the admin if he agrees they should be removed (e.g. the whole "вода з газом" thing, that's wrong and weird...)
The sentence is grammatically correct, but has a weird unnatural meaning. So let's just stick to this for now: якщо -> if, коли -> when, from the point of view of grammar, not meaning :(
I'll put it this way: "it is raining" in Ukrainian is "падає дощ" or "іде дощ". Even Ukrainians themselves argue which one is more correct (and probably it has to do with Polish and Russian influences in the language, where it is: "pada deszcz" and "идет дождь" respectively). And if you take "падає дощ" for "it is raining", than you can understand "іде дощ" as something slightly different - it will rain in a moment, therefore: "the rain is coming".
Two of the examples provided by you mean "it is raining (presently, currently)". "The rain is coming" is a bit of an unusual phrase, I'm not sure I ever heard it used in that sense before. Might be a different dialect of English that you speak ( I speak NA English). But in Ukrainian if you want to say "it's about to rain" I would use a phrase "ось-ось піде дощ", "зараз задощитиме". I certainly wouldn't use "іде дощ" if it's not raining yet.
I checked it and it appears that the phrase "іде дощ" is indeed understood nowadays only in the same way as the Russian "идет дождь" (i.e. "it is raining") and not the Polish "idzie deszcz" (which means "the rain is coming" - like in... "the winter is coming" ;) ). At the same time, you can still use both: "Russian like" "идет дождь" and "Polish like" "падає дощ" for "it is raining". I guess that's it, topic closed :) PS. Sorry for the mix-up.