The unanswered questions were a big reason I replied in the nature I did. It sounds like OP is at the beginning of this process, and is looking for guidance in where to go next to answer those questions in the first place.
I am happy to report that with my cameras coming in over USB (one with an HDMI capture dongle), I have had absolutely no problem with latency issues or USB limitations with more devices. Hopefully, that will give OP a little confidence to at least try some of those options, in the event they work- before going to some heftier video setup/gear.
If there is some latency, syncing with audio may be the tough spot, obviously. On one video source, it might be perfect- then get thrown off when the audio stays constant, but video shift on source change. More as a not for OP< I would say work on getting video synced up properly- THEN worry about getting the audio synced with it. Since I assume the audio will come into the computer independently of the video (Not part of a webcam or other such input), hopefully this won't be as much of a headache.
But yes, there are some concerns here. Don't be afraid to try it out without top-end gear, to see if it suits your needs. I've had remarkably good results with just a few webcams I had kicking around, an SLR, and an IP cam. (I ported in the IP cam on a browser, but am now actually using a webcam running through the Raspberry Pi I use to control my 3D printer, and bringing it in as a VLC source. The added bonus is it is easier to move anywhere I want, as the RPi is wireless, and I can power it with a decent sized power bank battery that can be moved around easily. This way, I can have a wireless cam in my chicken coop if I want! No power cables to the coop! :) )