What is this mystery process: "-i"?

The best way to find out is to note the Process ID (PID) listed in Activity Monitor for the mysterious "-i" process.

Then open Terminal.app and execute the following command:

sudo lsof -p 1234

where 1234 should be replaced with the PID number you've found in Activity Monitor.

The lsof command will give you a list of files that are opened by the mysterious process. The first line of output will tell you the "cwd", which is the current working directory of the process. It is probably not going to tell you much.

The second line of output is usually a "txt" file descriptor that will tell you the name of the executable (i.e. the program) that is running in the program.

This should tell you which program is running as "-i".