Dear support team

I have an already existing site at www.giorgiofatouro.gr and I want to create a new website with absolutely different content/ template etc.
So what I would like to ask is if multi sites can help me and if it is suitable for the already existing site.
I also would like to know if I have to do somehting (such as a backup) at the already existing site before installing multi sites extension

Create a website with another domain is absolutely possible.
JMS can recognize websites with different domain name or subdomain name or even subdirectories.

Concerning the "import" of an existing website as a slave site under JMS, this is possible but is a manual task.
The requirement to important an existing website is that you have all the extensions required by the slave site that are already present in the master with exactly the same version number. The reason is that slave site re-use the PHP code present in the master. So it must be present.

If this is OK, then you can declare the slave site in JMS and re-use the DB from the standalone website.
The potential remaining things that you may have to import are the specific files likes images, video, ...

Theorically, JMS should only be installed on a master website and never have to be installed in a slave site. The only exception where you may have to install JMS in a slave site is when you propose a website creation from the front-end of the slave site.
Otherwise, JMS is not required in a slave site and when it is installed, some functionalities are disabled.