Is it possible to hide it? I'm developing a webpart for a special page and it shouldn't be possible to place it somewhere else.
To "hide" it from the WP gallery you just leave out provisioning the Web Part Control Description file (.webpart) (in VS2010 - just remove the .webpart file).
You will still be able to add your Web Part in server side code or by directly adding it in the WebPartZone in the page (via a feature that deploys the page or using SPD customizations).
PS: To stop people from exporting it make sure that you override the Export property and always return that it's not exportable