Remove the http from sent emails

With all the versions of hikashop, you can modify all the text that is used by going in the config under the tab languages and editing your language file. So you can override the text string:
THANK_YOU_FOR_REGISTERING="Thank you for registering at %s."

and put:
THANK_YOU_FOR_REGISTERING="Thank you for registering at www.drverde.ro "

It's the same for the order notification email.

With the Business edition of HikaShop, you can customize the emails via the menu System->Emails.
There you could edit the user account email and change the line:
echo JText::sprintf('THANK_YOU_FOR_REGISTERING',HIKASHOP_LIVE);

to:
echo JText::sprintf('THANK_YOU_FOR_REGISTERING',preg_replace('#https?://#','',HIKASHOP_LIVE));

That would avoid having to change the translation strings when changing the URL of your website since it would still be generated automatically.

You can switch without any issue. All your data and configuration will be kept.

In the option "Order creation notifications email address" of the config under the tab mail, you can just put several email addresses separated by a comma.

the files are available in the folder media/com_hikashop/mail
but please note that the emails will be updated when you update HikaShop so you will have to backup the modifications and reapply them, unlike when you edit the emails via the interface.