I see you are still referring to them as Japanese 'symbols'. I started a thread about the Japanese writing system with someone new to IDN's such as yourself in mind. You can find it here: The Japanese Writing System
You might want to study that for a bit.
As to your comment: Yes the Japanese can read and remember Japanese. That is the entire point of names in their language. They understand Japanese much better than English as can be expected. The people who live in the place called 'Japan' speak,write and read 'Japanese'
Do the Japanese recognize and understand what a domain is in Japanese?... Yes they understand. They have been branding their websites with Japanese domains for years now.
Please dig into the archives of this forum a bit. All will be made clear to you with a bit of research.