Yes mate all one room
When Virtual desktop connects what bandwidth does it say on the top of the window where you change the settings? And do you mind me asking what router do you have? Exact make and model please if possible.
Your problems sound exactly like what you would have if you didn't have a good wireless connection. If you are in the same room and are connected at 5Ghz and the cable between your router and your PC is Cat 5e or higher, then it's either a really crap router or a faulty Pico 4.