Have a look here, big list:
https://wiki.gnome.org/Apps/Rhythmbox/Plugins/ThirdParty
I've worked on plugins related to tray icons and album covers.
It's been a while since I used RB so I don't know if they work any longer, sorry.
But I believe fossfreedom still works actively on a whole bunch of plugins all the time.
In Ubuntu
apt-get source rhythmbox
will download the source code for Rhythmbox.
If you want to contribute to Rhythmbox you should get the original source code instead. See https://wiki.gnome.org/Apps/Rhythmbox/Contributing
I use Spotify generally, cmus for local stuff. If you want one that blends well with GNOME 3, Rhythmbox with the alternative-toolbar is probably your best bet.
MTP needs to be supported by the USB controller. Most only support UMS.
However, what you <em>should</em> be doing is putting a file called .is_audio_player
in the root of the device to let Rhythmbox (and other applications) know that they should manage it as a media player. The format of the file is very underdocumented, but here's something.
Not wireless but maybe useful:
My android phone mounts over USB as a storage device, so I use the trick where you make a hidden file called ".is_audio_file", that tells rhythmbox where to store music on it. The I set up a sync playlist in rhythmbox and set that to sync to the phone. This is not well documented,
https://wiki.gnome.org/Apps/Rhythmbox/FAQ#How_do_I_set_the_music_dir_in_an_external_device_.3F
Some examples https://cgit.freedesktop.org/media-player-info/tree/media-players
Music player is rhythmbox and I'm running native steam. I don't run any applications in wine (except for league of legends). Rhythmbox is default in gnome and its nice because of how well it handles plugins, but I'm thinking of using replacements like 'banshee' soon
Rhythmbox has a lyric pane. It's not there by default though, you have to add a plugin. There used to be an edit button too, back when you were allowed to edit LyricWikia. Not certain but I think you can configure it to look in a local directory first, so you could save your lyrics there.
https://wiki.gnome.org/Apps/Rhythmbox
Those are a few that I've used in the past, but now a days I just use Google Play Music with the All Access subscription. I upload music that I get from Steam, GoG, or what not. I can create a playlist during lunch break and have a nice playlist for the drive home.
I'd recommend using mpd or rhythmbox instead of banshee. Both handle large libraries with no problem at all.
For converting file types, you'll have to use external tools. Though this is gradually disappearing, the UNIX philosophy is still quite strong in software: "do one thing and do it well". Therefore most music players won't do anything beside playing music. You'll have to convert your files using mpg123 (here's an example).