The first picture shows Server Link configuration. See this post for more details: Server Link explained
Yes, the "Server command" action requires a connector to EM Server. Each connector can connect to 1 space only.
The "Call another module/project" action doesn't "know" about spaces. It refers a project by project path (absolute or relative). If you need a project to run a space task, use the "EM Command" action.
Alternatively, you can use a parameter to provide a project with a path to another project that may happen to be in another space. But that can be inconvenient, because by default the file picker in Server UI doesn't allow picking files from public folders of other spaces. You can enable picking files from the whole disk drive, but that can be undesirable from a security perspective if untrusted people can run the task.
The "Run task" command in the "EM Server command" action identifies a task by an internal ID rather than a name. That's why it doesn't support parameters. Two tasks may have the same name but different IDs. So that won't work.