memes

We do the opposite. If something is known we just say it.

"The girl(1) is playing(2) violin(3) downstairs(4)"

دختر(۱) در طبقه‌ی پایین(۴) ویالن(۳) مینوازد(۲)

To refer to an unknown thing we add a prefix ی to the thing

A girl -> دختری
The girl -> دختر

Don't know about Farsi, but in Russian you would have to declare your knowledge and specificity of the subject. You can transmit some of that information by changing word emphasis, but it's not very clear.

As for your sentences I would translate them as:

1. The girl downstairs was playing violin → Девушка [girl] внизу [downstairs] играла [was playing] на скрипке [violin].
2. A girl downstairs was playing violin - Внизу [downstairs] девушка [girl] играла [was playing] на скрипке [violin].

The first one puts more emphasis on the "girl". The second one puts more emphasis on "downstairs", almost suggesting that the identity of the girl doesn't matter, kinda "some girl who happened to be downstairs". But it is not as explicit as a definite/indefinite article for sure.

If you want to make it certain that the identity of the girl doesn't matter, you could use an adjective to that extent: Внизу [downstairs] какая-то девушка [some girl] играла [was playing] на скрипке [violin].

If you want to make it certain that both you and the person you're talking to know about the girl, you can use a determiner: Та девушка [that girl] внизу [downstairs] играла [was playing] на скрипке [violin].

I guess the is implied, count is explicit. A thing becomes one thing and the thing becomes thing.

It's not that hard once you understand the difference. It's more like getting a feel for it than following an actual rule, but a good starting point is that が indicates the subject of a clause, whereas は indicates the topic a sentence is in reference to, which can often also be the subject of the primary clause, which is why they get confused.

For instance, 私が疲れた (watashi ga tsukareta) would mean "I am tired" literally, but it would sound awkward, because the more usual way to phrase this would be closer to "as for me, tired" or 私は疲れた (watashi wa tsukareta).

It's not a perfect rule, and there isn't a perfect way to directly translate it because English (and most European languages) don't have a comparable grammar structure. But generally if you're speaking in reference to yourself or another person, the correct particle is usually "wa", but not always. It just takes practice to get a feel for the exceptions.

And often enough "wa" is used instead of "ga" for objects and places, but it's easier to get a feel for the difference. For instance, さっぽろが寒い (Sapporo ga samui) and さっぽろは寒い (Sapporo wa samui) are both correct, but have slightly different meanings, although the English translations of both would sound the same, "Sapporo is cold".

The difference is that with "ga," it's more like an isolated statement of fact. On the other hand, with "wa" it's usually being contrasted with something, often implicit and unstated, carrying nuance like "as opposed to where we are" or "as opposed to the rest of Japan" or "as opposed to our other options for a travel destination", but what exactly it's being contrasted with is usually clear from the context of the conversation.

At the end of the day, "ga" is usually cut and dry: it marks the subject of a sentence the same way "wo", "ni", "he", "de", etc., mark other grammatical cases (direct/indirect objects, prepositional phrases, etc.).

"Ha" is the only one you need to watch out for with its very distinctive Japanese-ness. Although Korean has a very similar construct.

Simple as.

I prefer dealing with complicated but ultimately rule-based stuff like は/が over the utter nonsense that is grammatical gender (and I'm German).

Edit: and because I see heated discussion about it elsewhere: grammatical gender is a very convenient thing to have (not to learn) and I wouldn't abolish it (just wouldn't want to learn it).