What is the best way to organize the separation of video and audio signal to different devices?

Question

WiFi

Given:
1. Epson projector (with hdmi interface) with the option to connect wi-fi adapter ELPAP07;
2. Active monitors with a mixer;
3. Wireless network;
4. Laptop
Question:
Is it possible to play video on a laptop using a third-party device (like a network media player) connected to the projector's hdmi interface in such a way that the picture is sent to the projector, and the sound from the laptop's sound card to the mixer?

Answer 1

Well, if connecting a projector to a laptop via HDMI is not an option at all, then any network media player that can use XBMC, or WiDi via an Epson adapter. Just on a laptop, you will need to tell the player that the sound should be output through the local analog output.

Answer 2

There is a class of devices called HDMI audio extractors.
They cost from $15 to $100.
Even the cheapest ones usually have a stereo RCA output, an optical audio output, and a passthrough/stereo/5.1 mode switch.
The only thing I didn’t quite understand from your question is that at first it sounds like you need to extract sound from HDMI and send it to an audio mixer, and video to a projector, and then you write that “sound from a sound card”. If the sound is already from the sound card, then connect it directly to the mixer.
Well, or more clearly describe what needs to be connected to what and on what interface.