Power on and start a terminal automatically at a specified directory
I would do this in two steps:

Open terminal on log-in
To do this, go to Apple menu &gt; System Preferences &gt; Users &amp; Groups &gt; Login Items and add terminal there.

Run a specific command when terminal is launched
Open Terminal, go to Settings &gt; Profile &gt; Shell and in the first box write the command that you want terminal to run. In your case something like cd ~/Desktop.