Is there a desktop calendar software with all these functions?

duleding, you wrote:

Yahoo or Google Calendar with automatic backup on the local PC;
View weekly
Box on the desktop, with the support of the function of auto-hide.

I am very impatient software such as a calendar.

Yes, you need konfabulator. (Now called widgets yahoo)
Download it from
Www.konfabulator.com
And install the widget yahoo calendar.