With the Nintendo Switch it is recommended to connect it to the internet with a LAN cable, unfortunately I don't have this option because the router is in a different room.
1 question
Does the Nintendo Switch recognize a Wi-Fi socket as an internet source?
2nd question (if the Nintendo Switch does not recognize it)
WLAN sockets also have a LAN connection
If I connect the Nintendo Switch to the LAN port of the WLAN socket via a WLAN socket, do I get a connection that is as good as with a LAN cable directly on the router?
No, she doesn't recognize that. But with the Switch it doesn't matter how fast the internet is.
Yes
no / probably, if your Wi-Fi socket is only a repeater, then nothing usually changes than if resourcefulness establishes the connection via Wi-Fi, if it is a DLAN solution then the connection could be better (or even slower, depending on the Wi-Fi and Dlan at your home)