Does this literally parse as "Now, rain is raining"?
Or "rain is falling-from-the-sky" or "rain is precipitating".
Kar (snow) and dolu (hail) can also yağmak, so yağmak is not just "to rain".
To me it means "now rain pouring"
What is the difference between "yağmur yağıyor" and "yağmur" only, so we could understand the use.
"yağmur" just means "rain" as a noun. If you want to say that water is falling from the sky, you have to use the phrasal verb 'yağmur yağmak"
İs it ok to just say "şimdi yağiyor" or does it have a different meaning?
It doesn't really mean anything without context. You must state what is falling from the sky in Turkish.