Is it possible to have blender save the single image when it finishes rendering it? I dont want to wait until its done as I let it render during the night. Ideally, I would want the PC to turn off as well when finished rendering. Thank you in advance.
You need to add a "file output" with the correct path in the composition workspace. The plugged image will automatically be copied to that place once rendering is done. You can add multiple file outputs so that the image is copied to multiple paths once rendered, or at differents steps of the compositing.
You can write a python script for the shutdown as explained by @WhatAMesh or alternatively if you are on windows OS, go into command line (Windows + R and type "cmd" ) and type "shutdown /s /t *" without the parentheses where * is the number of seconds you expect the rendering will take. I suggest inputting a greater value than what's expected.