Before submitting to dmoz

questions before submitting to dmoz:

1. can I submit my website with this title (just examples) ex: HQ Softwares if is already listed a website with that tilte ex: HQ softwares in the same category? (difference is S & s)
2. I'm the new owner for a website, the site now is redesigned, updated by me, how can I know if is not banned or was not submitted already to odp?

The instructions on the form are very clear.
Title = name of the company or if the site is not about a company the name of the website
if there are several websites / companies with the same name than they will be listed with the same name

Becoming banned is very rare and you should not bother about it.
If the site was laready suggested before and it has become a totlay different website suggesting it again is no problem.