I have a computer that has a video card supports Miracast (AMD RADEON RX 550), and the Samsungs TV also supports. I would like to use it as a second display, but I do not understand what you need. From everything on the Internet, I found out that the WiFi adapter is needed to the computer, you can not connect on the router, the adapter to buy? If “yes”, then connecting the Internet to a computer should be strictly for this adapter, or will it be possible by cable?

It costs Windows 10 1903.

Answer 1, Authority 100%

miracast is, initially, the standard for wireless connections (then beam wireless connections) between devices and displays.

here People with an almost identical problem – they want to connect the PC to the router by Ethernet to the router, and already from the router distribute the signal-display signal.
And in both cases, unfortunately, still need a wireless connection (Wi-Fi Direct) so that the devices can detect each other:

… Miracast Cannot Detect Devices Over Ethernet Alone …

“Miracast cannot detect devices only via Ethernet, without assistance”

… at this time, You’re Going to Need A Wireless Card In Your PC for Discovery Over Wi-Fi Direct. Once Discovery Is Complete, Your Actual Session Can Take Place Over Infrastructure, If The Right Conditions Are Met.

“Currently, you will still need a wireless connection (WiFi-card / adapter) in your PC, to detect the device via Wi-Fi Direct. Once the detection is successful, you can use “miracast for infrastructure” .

if briefly:
Without Wi-Fi whistle can not do.