> Our site sassyqarla is still not listed in DMOZ,
If you suggested the site it is most probably still waiting review.
Or it is rejected.
> we tried to suggest, but it failed.
What do you mean with "it failed". Did you get an errormessage, than it was not suggested. Did you get the confirmation screen, than it was suggested succesfully.
> Our EIC even applied to become an editor but he failed.
He will have received an email explaining why and how to improve.
> We don't know how can we be listed in the site.
You can't.
You can only suggest a site. That's all.