Behavior of eicar is not ‘always’ as the same as normal viruses.

No, it should work normally…
In Home version you can’t automate the actions (besides the ‘Silent Mode’ sending the file to Chest) but you should be able to manually take any of the actions.

Check if the avast plugin is not disabled into MS Outlook:
Outlook 2003 > Help > About > Disabled items
Outlook 2000 > Tools menu > Options > Other > Advanced Options > Add-In Manager

If this does not help, can you try to repair your installation?
Go to Control Panel > Add/Remove programs > avast! antivirus > Remove
Then choose Repair function in the popup window (Repair).
You must be connected to the internet while repairing.