If you want to use a command and the user isn't in your server, you can enter their user ID as parameter instead of their username.
To find a user's ID, you need to enable Discord's developer mode by clicking "User Settings" > "Advanced" > "Developer Mode" slider.
After enabling developer mode you can simply right click their username and click "Copy ID" button.
If you invited Jim after 24th of March, 2021 you need to kick him and invite back for slash commands to appear in your server.
This is due to Discord grandfathering servers that already invited at that point into having slash commands permissions for Jim, any server that invited Jim afterwards lacks the permissions Jim needs to display slash commands.
No, for some commands you need to have a specific permission.
Jim uses pure discord permissions to handle muting users, it creates a Muted role and creates permissions in every channel so that users with Muted role can't send messages. To make sure this works properly