What are exactly the legal consequences of "All rights reserved"?
Almost none. You have to explicitly grant copyright rights. You don't even need the Copyright notice for them to apply. My "almost" is because the notice makes it harder for somebody to argue "they didn't realize".
Do I still need an additional SW License Agreement or is the Copyright notice above + a Disclaimer of liability sufficient?
If this is free software (I know you said it isn't), do yourself (and everyone else) a favour by picking a license you like. Preferably either GPL or MIT (depending on your taste). There are far too many free licenses already. Please don't add another. (It also makes it much easier for any user of your software: "Oh yeah, GPL v2. We understand that. We can use it." as opposed to "What are the implications of using this one??"
As this is not free software, I think you need a paid-for lawyer (who understands IPR in your juridiction.)
Edit: In principle, I believe you don't need anything. The code is copyright, so the customer can't do anything with it (without explicit permissions that you haven't granted). However if the customer doesn't realize that or thinks you won't mind, you then have to go to court to enforce your rights (and probably end up with a disgruntled customer). A short, clear, license will make it clear to the customer what they are allowed to do, and save all that aggravation.