Q: 3 questions about Mac Appstore errors or bugs

1) I see iWorks products at the "Top free" category but why they are also written as "$19.99" instead of "Free"?

They are only free if you qualify in one of two ways;

a. If you purchased a new Mac since 1 OCT 2013, or

b. If you had previously purchased the previous iWorks suite, iWorks '09.

Otherwise, you must purchase them.

2) I already download OSX mavericks but why Mac Appstore showed as "download" instead of "Installed"?

The Mac App Store (MAS) sells apps. What you downloaded from the MAS was the OS X Mavericks installer (an app) that self-deletes after it installs OS X Mavericks on your Mac. So the installer is no longer installed on your Mac and is available to download again.

3) I have an app to upgrade, but if I click 'updates' category, it siad, No updates available. But I if found the specific app that I need to update from 'Top chart' category or 'categories' category, it showed as "update" instead of "Installed"...

The MAS relies on Spotlight for an accurate idea of what is installed on your Mac. Perhaps your Spotlight index of your HDD is out-of-date or corrupt.

Re-index your HDD.

Spotlight: How to re-index folders or volumes -

http://support.apple.com/kb/ht2409