https://lyricstraining.com/ja/ for Japanese, but no Russian (yet)

Lots of other languages (choose on the right). Choose genre in the left.

The only Russian pop group I can think of right now is Tatu (t.A.T.u.) but I think they split.

As for Japanese bands/artists, I love Kalafina, Ali Project, Utada Hikaru, and SID the most. I would definitely recommend "Sakura Nagashi" from Utada Hikaru, "Magia" and "Oblivious" by Kalafina, "Rain" by SID, and "Angoku Tengoku" by Ali Project.

Unfortunately, I don't know any Russian bands.

I like http://www.russianradio.eu/ (There's also an app: "Russian! Radio")

I also listen to Юмор FM through the app called "Radios Russian" (or http://www.radio.pp.ru/) There are a bunch of other stations too, but they often don't load, and most of the stations play a lot of music in English while Юомор doesn't.

Ari No Mama De by Takako Matsu is one of my favourites. It's the Japanese version of Frozen's Let It Go. Besides that, I don't really listen to other Japanese or Russian songs (although, I would like to!). Hope that helps :)