I run the server with Oxide in a container. Server and Oxide turn on and work properly. I have a problem with sending any command to the server console. Commands are sent to the container on /dev/stdin, but Oxide does not respond to them. The same commands work in console when I run the server on a PC.

The console only works on Windows, it won't on Linux; there isn't one for it. I'd suggest using an RCON client when hosting on Linux.

Ok, I also tested RCON, but it does not return any responses, although it does execute commands. Will it always be that way?

It depends on the command you are using, but right now universal command replies are not always caught by RCON clients because of how they handle responses.