Usually, Parked Domains are used to have more than one Domain Name for the same website. In other words, a Parked Domain will display the exact same content (website) as the Hosting Account's Main Domain. Additionally, a Parked Domain can be used to make Email Accounts too, so this is a great solution if only need to use the Domain ...
Your Email Accounts details can be located by accessing your Control Panel and navigating to the Details menu.
You should be able to install your own webmail client, but we can not provide any help in installing and configuring it. You would have to ask script authors to help you with that!
Currently, Emails are not backed up automatically like your website's files and databases on ultahost.com. The best solution is to locate any emails you've saved up locally. For example, Outlook will keep emails stored on your Computer, separately from the email stored on ultahost.