I have a Logitech bluetooth keyboard + mouse combo as well as a blue tooth game pad. If you're looking to get a Dex station, don't bother with the official Samsung one because it's way overpriced. Get this one instead. Works just as well
I contributed to a few threads on it. Works great. I see a lot of potential.
I bought this one. There appears to be a 60% off so it puts it under 9 bucks for a working dex adapter. Daaang. I paid more than that. I do like the form factor of OP's better.
I bought PCL, black PCL dye, a 40mm USB fan, and I'm gonna make my own stand with it and a usb3 hub. It'll have strong cooling (will probably emulate and maybe Planescape), and a miniUSB-cable for a DualShock3.
I use a triathlon Bluetooth mouse and Logitech keyboard. No lag on either.
Don't buy the DEX pad its stupidly overpriced. This alternative works just fine.
Your best bet is to return the HDMI converter and get one of these: https://www.amazon.com/dp/B0721483XM/ref=cm_sw_r_cp_apa_5xyBzb8ZSHNTP