Is 18 levels for example enough in a puzzle platform game to release a Alpha to the public?

It depends on how long each puzzle takes to solve. And really, if it's explicitly a pre-release alpha, then I wouldn't see any reason not to release any amount of work you've got.

It depends on what you are hoping to achieve by releasing it early. If you are just releasing it for the sake of releasing it, I would hold off. However the phrase 'test early, test often' definitely applies. If you are hoping to gather player feedback and use it as direction for improving the game, an early release is not a bad thing. In fact, I would say that 18 levels into a puzzle game may actually be a bit late to release and get feedback from players.