Hello. Multicorder can record master or input of the source. If you need to record separate your mics you need to assign a separate audio bus per mic. For example for mic1 bus A,for mic2 bus B,mic3 bus C,mic4 bus D. etc. Then.. You will go vmix-->settings-->outputs/ndi/srt and in an output 2 (or 3,or 4 if you need the 1-2 for anything else) you will press the cog and in the audio channels you will select MABCDEFG. Then in multicorder check to recored output2 will record all the audio channels and channels A,B,C,D, will record each mic audio. Be aware to these buses A-D not to assign anything else than per assigned mic in order to have clear audio from this mic.Also you can select wav button to have separate wav audio channels.Also be aware from the limitation some record formats have. For example if you record mp4 you cannot record more than 6 audio channels.
Other way is to do the audio channels record via the normal record and in the audio select the channels,you need and a proper format to do it.

I dont know if possible. you have 3 cameras and 1 pgm. So you need 4 files. The most simple way i believe is to record your cameras and plus in other output separate wav files. Then in post production you keep your cameras and use the wav separate file.

Depends on what you're using your buses for.

As of right now, the only 4 channel options for audio recording are MA or FG.

If you have those free to use, that's going to be how you do it. You can use the audio matrix and presets to separate the 4 mics into the 4 channels.

Since you have multicorder, I assume you have the vMix edition 4K or greater.

The 3840x2160 option is 4x 1080p.

What you can do is designate a single output for recording, set that use your MA or FG, and create a multiview at that output with the 4x preset and use your 3 cameras as the first 3 layers, leaving #4 blank.

You can then break it up in a program like Handbrake or even whatever video editor you use.

That'll give you 4x 1080p videos with 4 channel audio in a single recording. (It'd also allow you to add a 4th camera to go along with your 4th microphone, if you so choose, while only using a single output.)

If you don't have MA or FG available, there are other options, but, as you said, this would be the easiest way to do it.