Apple Music

Cannot add any track in Apple Music app. When I press the plus ➕ it showed that song added, but in a second the plus icon returns back and the song is not adding in my playlis. And that way i have no possibility to save songs.

:Hello and welcome to Apple Support Communities

If I understand your post correctly, you are adding songs to your Apple Music Library but they are not adding to your playlist. I'd like to help.
You can add music to your playlists like this:
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Create a playlist

You can create playlists on your iPhone, iPad, or iPod touch; your Mac or PC; or your Android phone.

On your iPhone, iPad, or iPod touch

1. In the Music app, find a song that you want to start your playlist with. Long press or use 3D Touch on the song, then choose "Add to a Playlist" > New Playlist.
2. Give your playlist a name, description, and cover image, then add more songs: Tap  Add Music, then search to find a song from your Library or the Apple Music catalog, or browse through songs under Library. When you find a song that you want to add, tap  .
3. When you're finished adding songs, tap Done.

By default, songs that you add to playlists don't automatically add to your Library. If you want to add each song to your Library, you can change your settings.

On your Mac or PC

1. In iTunes, find a song that you want to start a playlist with. Move your pointer over it, then click  and choose "Add to Playlist" > New Playlist.
2. Click Library at the top of the iTunes window, then click your new playlist in the left sidebar. Click the name and cover image to edit the title or add an image. If you want to add a description, click  , then choose Add Description.
3. Add more songs to your playlist by searching or browsing your Library or the Apple Music catalog. When you find a song that you want to add to the playlist, click  and choose "Add to Playlist" > [your new playlist].

By default, songs that you add to playlists don't automatically add to your Library. If you want to add each song to your Library, you can change your settings.

See the full article here:
Create and share playlists
Let us know if that resolves this issue for you. 
Thanks for using the Apple Support Communities.