Off the top of my head, first the current question:

The currents on the east of Arya and Katar are a place to look at. Your gyre here sweeps out and around the island east of Arya and then continues east. It could track around the west side and east side of that island and continue north to form a single gyre that cools near the arctic and sweeps back south on the west coasts of Sakura and Ystar. Now what you have could be correct, there is nothing impossible about it (it might even be likely) from the limited knowledge of the world climate, but the main thing is to be aware of the possibility of going the way I mentioned for climate choices. The more I look at your map, the less problem I see with how it now sits. The importance here is one of the major tenets of climate, warm waters evaporate and create moisture/rain faster and easier than cold current waters. The west coasts tend to be cooler and east coasts tend to be warmer, although this is naturally mitigated by many factors. Winds blowing onshore from a cold current will carry less moisture than those blowing in from a warm current, a good thing to think about all over the world.

Note: I'd be curious to see your tropics of capricorn and cancer put down for better reference of that zone.

Now onto your climates. You seem to have a lot of rain shadows unaccounted for. For instance, Tarantia. There is a mountain chain there that begs for something. At that latitude most likely your major storm systems are moving west to east with the jet stream. We've no real clue of the terrain heading across the bulk of the continent, so all is good until you hit those mountains. At this point any moisture left in the air is going to dump, creating a rain shadow on the east coast. Now this could be mitigated by tropical storms coming up from the equator (like the east coast of the US which pulls moisture from these tropical cells as well as the warm coastal waters) except that unlike the eastern US you have Naila down there that would likely inhibit tropical storms reaching that rain shadow zone. More likely any tropical storms would track to the southern coast of Tarantia (possible hurricane zone, although Ningya could deflect a little of that energy) and drive moisture laden air into the middle of the continent, as occurs in the middle of the US. In the midwest rainy years are often brought on by tropical moisture from the Gulf of Mexico and not simply brought in on the jet stream.

Both Fellion and Gaya also seem to have mountains begging for rain shadows. Again, these look like they would fall into a west to east storm track with the jet stream, so you are looking at rain shadows on the lee (east) side of those mountains. And the little brown coastal area of Fellion would likely flip-flop with the green to the west, as you have a warm current on its east coast. And that rain shadow could be mitigated by tropical moistures coming down from the equator also, so the rain shadow wouldn't necessarily be desert.

North of the mountains on Sakura would be damned cold and dry. The area of water and land surrounded by Tarantia, Arya, Katar and Naila would be interesting.

One of the most interesting deserts to look at is the Atacama, which sits on the coast in Chile where fog is the main moisture it gets, and it is a great example of cold currents messing with things.

I could probably prattle on much longer but that will do for now, LOL.