Is there any software I can use for exporting my database (tables, relations) from Mysql to a visual view that I can use in my documentation?

You can use Toad World it powerfull.

did you try to look for mysql tools on mysql website? Try to use mysql workbench and mysql for excel

actually there are lots of softwares where you can export or import your data from your platform like informatica, Apex data loader Eclispe