Welcome to the forums
I am showing cPanel 10.2.0-R25
The techs can normally transfer your site for you since you have cpanel.
The stats are in your home > tmp > awstats folder.
If they do not transfer, just copy them over.
There are many wordpress users here and can offer help if you need it.
You can open a help ticket (link at top of page)
and ask the techs to park another domain on top of your account, no charge.
You of course will have to point the other domain to the DNS in your welcome e-mail.
As to support for your account for server problems, there are techs from all over, so the time should not matter.
If you need help with third party scripts, you can get it here from the family members.
If you have any other question, please ask.