Audiences are indeed not real security  - anyone with the direct URL to the list
or item (or access to search for it) will see it.

You cannot target  content and group  by date, but you can target a web  part (like
you do in #2) and group by date  within that part  (like #3) which means people
not in the audience  won't see the web part at all, and those in the audience
will see the content  grouped by date.

I cannot target  content and group  by date.

When I target content  and group by Audience the web  part is displayed like this.

Audience 1:
listing A
listing B
listing C
Audience 2:
listing D
listing E
listing F


What should i do if i don't want to show "Audience 1, Audience 2".

You don't want more than 1 audience  to appear, or you don't want the labels to?
If it's the former, just setup the targetting in the web  part to only be 1
audience. I don't think there's any way to do the latter, except to write your
own web part  or (maybe haven't tried this) use FrontPage to convert the web part
to a Data View and edit it that way.