As Styles said this is correct behaviour.

Yes, it is intentional that you can own 0% of your company and still be CEO (this is also true of real life). You only get kicked out when someone else owns 50%+ of the company.

In terms of buying your own shares back - this is also the correct behaviour. If you own 0% of shares then why would a share buyback increase your ownership? You have to own some shares in the first place to benefit from it. A share buyback simply decreases the number of shares that can be sold to the public (or takes the shares off someone else, making your existing stake bigger).

It then gets completely bugged. When you buy back your shares with the company, your ownership will be still zero. Only if you buy the shares back with your personal wealth the ownership gets properly transferred to the player but then the company cant actually trade its own shares. Basically completely broken.

Your company will also keep all of the capital from the sells. So right now I am building real estate with money of a company I have no shares in.

Just start a new game and sell all of your shares within your primary company with no subsidiaries ever created. You will still be a CEO and a chairman.