You ask smart questions.
Yes, it would be saved because the changes you would be making would be applicable to your current drive and installation, not to the Media you booted from.
This would be done with a series of terminal commands which I do not remember tham all off the top of my head in spite of doing it several times- I would need to look for a step by step guide.
To answer your "how" question, when youa re booted into the installation Demo media, that would be on your Optical drive or your USB- Let's say USB, so that would be sbd1
Your primary drive is usually sda1
See?
So in terminal, you could mount or unmount your primary while booted into the USB drive with
sudo mount /dev/sda1
and
sudo umount /dev/sda1
Yes, I seem to be having a moment here where it pours; I am also doing the shop and and it seems I cannot finish answering one question before another person comes up with a new one. Bouncing between answering the proper gear ratio for the speed gear for a Dana 7:62 and vgscan is a bit mind bendy.
ahhh... almost forgot: