Long time lurker, thought I'd chime in -
Just in case anyone is still wondering how to do this:
-Install iTunes (the .exe - not the version from the Microsoft Store)
-Install foobar2000 and the Free Encoder Pack that comes with foobar2000
-Enable ALAC encoding in MusicBee
-Select C:\Program Files (x86)\foobar2000\encoders\qaac.exe for the encoder location
-Use the following encoder options:
--ignorelength -s --no-optimize --alac -o [outputfile] -
-Do a test track to make sure it encodes correctly
I believe it will also work with refalac.exe that comes with foobar2000 if you do not want to install iTunes. The only difference is that "refalac" is the standalone encoder based upon Apple's open-source code whereas "qaac" is the real deal that comes packaged with iTunes. I have never heard of there being any audible difference.
As for keeping your backups in FLAC vs Apple Lossless - it depends on what you are using for playback. If you use Apple devices, I would suggest staying with Apple Lossless and using FLAC if not. You do not need to worry about "error-checking" as long as you keep redundant backup copies of your library on an external HDD for example.
For AAC files, stick with qaac or fdkaac for your encoder. fhg, ffmpeg and Nero are outdated AAC encoders that do not have the same sound quality. I'd even argue LAME MP3 is a better encoder than those.