My iPhone cannot access App Stores!...Part II

I called Apple Inc. Apple ID support center.
They said that the Apple ID was not available, because an ID is not formatted mail address style.
Umm.. My Apple ID is not use.

And they asked me "Do you have account with ~@mac.com?"
I am reminded the "mac.com" account possessed it, and I do login iTunes Store with the "~@mac.com" mail account.
When the login OKAY, it's successful!
I try download from the iTunes Store, but fail the download.
The system shown alert my mac.com account  is not matching personal identifications then I have to input more information for the account management system.

In the first place, how access to the "~@mac.com" mail to receive?
It seems to take time a little more.

My iPhone cannot access App Stores!

When update iOS 6.0 --> 6.1.

"This Apple ID has not yet been used in the iTunes Store."

My iPhone cannot access App Stores, but able update installed applications. I bought my iPhone in November, 2012 and it has not problems to access for the App Stores.

古の(inishie no)Apple ID

My Apple ID has created over 10 year ago that is not "mail address" format.
.Is it causes? Apple co.