I think he is the most famous artist in Japan.

I have been waitinglistening to his song forever.

I think he is most famous artist in Japan.

I think he is THE most famous artist in Japan

It is very sad song, and very emotional.

It is A very sad song, and very emotional

I have been waiting his song forever.

I have been waiting FOR his song forever

My fFavorite aArtist

I love his song, "Junk".

It is very sad song, and veryand emotional song.

I have been for waiting his song forever.

My fFavorite aArtist

I think he is the most famous artist in Japan.

I love his song, "Junk".

It is a very sad song, and very emotional.

You could also say "It is a very sad and emotional song."

I have been waiting hisfor his (?) song forever.

I'm not quite sure what you mean here. If you're referring to the song you already mentioned, you could say "I have been waiting for this song forever." if it came out recently. If it wasn't a recent release, you could say "I waited for that song forever."

My fFavorite aMusic Artist

(1) Generally, all words in a title are capitalised. Minor issue though.
(2) "Artist" is a very broad term. It'd be good to specify explicitly that you're referring to music artists in particular.

My favorite music artist is Kenshi Yonezu.

Same as above.

I think he is the most famous artist in Japan.

I love his song, "Junk".

A space is placed after commas.

It is a very sad song, and very emotional.

I have been waiting hisfor his (new?) song forever.

(1) The phrase is "wait for (something)".
(2) It's not clear what song you're waiting for. Are you referring to "Junk", another new and upcoming song, or something else? It doesn't make sense to wait for "Junk", since it's already been released, so I'm assuming that you're referring to a new song, in which case it'd be good to clarify this.