Let me start over... Need to be a bit clear about the what? 6 different setups... So - #1 = basic setup is to directly connect to the projector - fine and dandy shouldn't have any problems. #2 - setup with multiple laptops to the projector. #3 - Problem connection: is when you tried to hook it up as in #1 but now it only shows a black screen? Or was that an entirely different setup?!? 4 - situation resolved by basic setup? 5/6/: Problem: Forced to load software onto clients laptops but issue with audio...
First off - HDMI systems can have communication between the source and destination. It can also send audio through that cable from version 1.2 or so. Its possible that your/their cable could be bad or that the positioning of the 2nd monitor/projector was way out... Far to the left or right or up or down... If you have an image as your background as many do - then that should be displayed on the projector if everything is fine... If you have 'black' as the color of the background on your laptop in combination with the possibility that the positioning of that projector is 'way off' as noted then that could be a possible explanation too... A quick test would be to change the color of your desktop and the color out of the projector should change to.. If however you still only get back - then check the cables.
What I mean by way off is this - as soon as you start
THIS VIDEO you'll see that he'll be moving the monitors - it could be way off to the right, left, top or bottom! But technically I think they're all supposed to be 'next to each other.' If you can't see it in the window but you have a selection for it then you'll have to go into the "Change the appearance of multiple displays' and then select "disconnect" from the multiple displays drop down menu and then re-enable it. That should 're-center' that projector.
Setup #2 probably happened with a 'cheap' splitter and/or maybe bad cable... And possibly why you only got a single or few resolution settings if any. Many of these switches aren't made for high quality. Some actually have 'good' and 'proper' "pass through" that aren't effected by the unit itself, whereas others take the HDMI then process it and pass it out - limiting the resolution to what they could engineer... So - if you want a switch you'll have to definitely check the output resolutions its able to display. To combine all that... You should have one that either surpasses or at least matches what ever you need to display on; considering upgrades/downgrades different equipment, etc.
THIS ONE seems okay at 4K!
As I noted HDMI also has audio out - but you would need an audio extractor for that. And a side note on the audio - you'll generally only get R & L connectors and then a SPDIF out... Unless you get nuts and go for the full 5.1 out like
THIS ONE.