Easy one first, checking your voicemail remotely: Call in, when the automated attendant plays, press *7. You will be at the same prompt as if you were internal and dialed Intercom 777 - "Welcome to Partner Mail VS. Enter extension number and # sign......."

Announcements are pretty stupid actually. First, are you sure you want to use Selector Code 1 for the listing of extensions? That prevents callers from dialing extensions 10 through 19 directly from the automated attendant.

At any rate, log into the System Administrator's mailbox.
9 for programming
3 for Automated Attendants
1, 2, 3, or 4 for AA-1, 2, 3, or 4
1 for the Day menu
6 to modify the menu
Press the selector code that will go to the Announcement (you said 1 in your post)

The system will play the current setting for the selector code and ask if you want to modify it
9 to confirm you want to modify it
3 for Announcement
1 or 2 for Announcement 1 or 2
Press 1, and start recording after the beep
Press 1 again when you are finished recording
Press *# to approve the recording (of the Announcement)and the setting of the Selector Code

You are now prompted to enter ANOTHER selector code, but you are done with Selector Codes, so press *#

You are prompted if you want to re-record the Automated Attendant greeting to press 1. You want to keep that intact, so press # to save all Selector Code and Announcement changes

Remember that from an Announcement, you can't enter extension numbers directly to transfer to extensions, you have to first press *8 (or *Transfer and then the extension number. So make the Announcement say "For Fred Flintstone, press *8-10. For Barney Rubble, press *8-11. For......"