Registration form, registration type and registration link not appearing for anonymous user

I am guessing this is something specific to your site and installed modules. Do you have the Field Permissions module installed by chance? Can an anonymous user get directly to /node//register?

Das Modul Field Permissions habe ich nicht installiert. Yes, an anonymous user can get directly to /node//register. It's just completely unformatted. But it allowed me to register as an anonymous user. Yeah! :-)

I don't have the Field Permissions module installed. Yes, if I enter as anonymous user /node/<node#>/register I see an unformatted registration field and can register. Yeah! :-)

Is this a fresh install, or you are upgrading an existing install of the module?

Any other contributed modules enabled besides registration? If yes, disable those one by one and see if it makes a difference.

Another option is to install 3.3.1 and see if that works for you.

Worst case I may need a dump of your site to debug it - but let's cross that bridge later if we need to.

It's a fresh install at a test deployment. I had already tried the older version before this one came out. I was hoping the new version would fix the bug.

This turned out to be an issue in the custom theme that the OP was using.