My answers to the OP - from my own limited experience:

1. I only know software based on abc2midi, which has its severe limitations, idiosynchrasies and bugs. (EasyABC used abc2midi last time I checked, maybe that has changed?) A possible work-around is to use abc2xml, import the result to MuseScore and export it to MIDI. MelodyAssistant can import ABC and export MIDI for single-voice tunes.

2. midi2abc ditto, but fortunately there are alternatives: EasyABC with its own MIDI import has been mentioned, MidiZyx2abc is another one which I normally prefer due to its extra functionality. All that software has the intrinsic limitations mentioned above.

3. If "mus files" means MelodyAssistant files: the software vendor claims ABC support, but limited to single-voice tunes. I think someone mentioned that the quality is not too good. The software is older than the current ABC standard, if I am correctly informed. (ABC standards seem to be a bit of a tragedy as well, given the fact that so many Mudcatters rely on it. I would appreciate if the experts kept us informed.)

4. To "write the lyrics under the notes on the stave in abc, at least for verse 1" amounts to "WYSIWYG". I do not know of any dedictated ABC software of such ambition, though EasyABC has taken some modest steps in that direction. Fortunately there are many "WYSIWYG" programs around, notably the free MuseScore. You can enter your music there, then export to MusicXML, then use xml2abc to obtain a surprisingly correct ABC represntation. If your favourite "WYSIWYG" software does not export to MusicXML, you are much worse off: you can use the MidiZyx2abc method (as I sometimes do), which can become tedious in complicated cases, but I still find it much easier than typing those w: things by "trial and error".

I have the feeling that ABC support could be better in the future. It goes the rumour in the MuseScore community that it plans to offer direct ABC support to the newest standard.

Note that I am nothing like an ABC virtuoso, and certainly do not know all software. I would welcome any information from the real ABC connoisseurs.