LG UltraFine 5K Display connected to a MacBook Pro mid 2015 - Webcam/Mic/Speaker not working
Does the Monitor support webcam/mic/speakers from a thunderbolt 2 &lt;-&gt; 3 adaptor?

No.  According to the specifications, it's a Thunderbolt 3 monitor that provides connectivity.  You need a Thunderbolt 3 port.  The adapter only allows you to convert Thunderbolt 3 to 2 or 1 but it doesn't give you any more bandwidth than what you have on your existing MacBook.
You have enough bandwidth to drive the display, but not enough to drive all the peripheral devices connected to it.