Thing is, we have a separate server - where the nopcommerce folder is, and a separate person who is working on it. I can access the store interface, but not the web site or the folder.
So, don't have a way to reach the .txt file, where do I find the SQL database? Can it still be done?
No, you cannot do it if you do not have access to the server.
If you have remote access to the server. Like Administrator and Password, then you can reach the server and make the backup of all stuff.
In future always ask your developers to provide access to the server otherwise if you have any conflicts you will be dependent on a developer!
And register VPS server or hosting & domain name ONLY to your account on you real name and just provide the logins to the developer. In this case you will have access to your server and can change logins in anytime you like.