I have FTP account on server and an account as Magento user.
Is it possible with these codes to gain a Magento account with administrator privileges?
Yes you can.
from app/etc/local.xml get the database credentials and write a small php script to execute the MySQL command listed here https://www.atwix.com/magento/reset-admin-password-mysql/
then run your php script, et voila!
Short answer: NO.
Long answer: FTP credentials have nothing to do with the application.
And in Magento, the frontend users (customers) are separate from the backend users.
So having a customer account does not give you access in any way to the backend and the other way around.
Off topic: Did you find some FTP credentials and you want to take over someone else's website? :).
Short answer: YES.
Long answer: If you have FTP access, you can gain access to whatever you want. You can manipulate the authentication mechanism, you can hardwire a specific set of credentials to be accepted and grant full admin rights. You can build pages which will output what ever data you want from the database.