Does Olivia Holt actually run this page?

Yes, Olivia does run this page but there are others who updates for her that you'll be seeing.

Who runs this site?

Some of her friends and family including, Maddi, Her Mom and Morgan (Her Sister) and sometimes Olivia herself.

Why don't she answer me under "Guestbook" but the others do?

Olivia won't be using Guestbook to talk to everyone. She will be doing live chats when it's set up. But she do read your comments there.