Q:

MySQL database schema creator & owner relationship? For example user & media?

What is the best way to link two tables together if there is a creator and owner relationship between them? For example a user create a media file entry. A user optionally has an image / media file as a profile picture. I've built a schema with MySQL Workbench. But that way it doesn't work. The other tables: A project has one or many bugs, a bug has one or many comments. Both bugs an comments can have one or many images / media files. Thanks!

A:

Firstly:
Based on you explanation, you Database Design should be like this (UML notation):
 

a user create a media file entry.

So you have a creator_user_id as F.K into media. It can not be null and each media should have a creator. 

A user optionally has an image / media file as a profile picture.

So you have one-to-one relationship between user and media. You have two options:

move user id as F.K to media as profile_user_id and make it Allow NULL and Unique.
move media id as F.K to user as profile_media_id and make it Allow NULL and Unique.  

Both is correct. 
For example (second option), you can have a profile_media_id as F.K into user. It can be null. But it should be unique. Means that a media can be appears only in one user profile.
This design (second option) is not wrong. It looks a circular reference. But, when you are adding a new user with a profile image (at the same time), you should perform these actions in one transaction: 

create a user (and let the profile_media_id to be null)
create a media with new creator_user_id
update the new user profile_media_id

Secondly:  
Your second parts of design (relationships between media and post and bug) looks good. (based on your explanations)
However, I offer designing a whole external media management system for them (see my answer here).
EDIT
you can use something like below to create your tables:
SET FOREIGN_KEY_CHECKS=0; 
DROP TABLE IF EXISTS myuser;
SET FOREIGN_KEY_CHECKS=1;

CREATE TABLE myuser(
    user_id INT NOT NULL,
    profile_media_id INT DEFAULT NULL,
    PRIMARY KEY (user_id)
);

DROP TABLE IF EXISTS mymedia;
CREATE TABLE mymedia(
    media_id INT NOT NULL,
    creator_user_id INT NOT NULL,
    PRIMARY KEY (media_id),
    FOREIGN KEY (creator_user_id) REFERENCES myuser (user_id),
    UNIQUE (creator_user_id)
);

ALTER TABLE myuser ADD CONSTRAINT myusermymediafk FOREIGN KEY (profile_media_id) REFERENCES mymedia (media_id);

See MySQL test here. 

