In minecraft can the owner or a high rank see your private messages?

Yeah course, admin or any other higher rank can set an option to view any private messages in Minecraft as if its a public message to view. Going by experience atleast I'm not too sure if it has changed but I doubt it. Get off of the internet kid. Owners can see everything you say and do. Unless there's server modifications in place… ONLY the server operator would be able to see all communications, including private messages, within the server logs through the server console.

The server operator would also be able to communicate with anybody in-game through the server console as well (as it would be noted as "Server" in chat).

The server operator would be considered the founder & original admin of the game server. Other mods / admins added to the server would not have access to the server console unless remote access is granted through outside means.

Get off of the internet kid.

Owners can see everything you say and do.

Unless there's server modifications in place… ONLY the server operator would be able to see all communications, including private messages, within the server logs through the server console.

The server operator would also be able to communicate with anybody in-game through the server console as well (as it would be noted as "Server" in chat).

The server operator would be considered the founder & original admin of the game server. Other mods / admins added to the server would not have access to the server console unless remote access is granted through outside means.