THE.H

Hello! All of our hosting plans do include email so you can setup [email protected] email accounts through your existing hosting plan. We also offer SpamExperts filtering for free on both incoming and outgoing emails so you'll be protected from spam, UCE, malware, etc. from hitting your inbox.
Now if you prefer to continue using the Gmail interface it is also possible to associate your email address(es) that's hosted through us to your Gmail account. You can do that by logging into Gmail and then go to "Settings => Forwarding and POP/IMAP". This would be done once you create your email address with us in cPanel as you'll need your server name, password, and other settings.
Lastly if you did choose to host your email through GSuite you can modify your domains MX records (assuming we're hosting your DNS) through cPanel using the 'Zone Editor' interface.

You can associate multiple email addresses with your Gmail account,
and choose which one is used for each outgoing message.
It will send your messages directly to the recipients (not via Hawkhost).
That is all handled within Gmail, and this Google search result (or some variation of it)
https://www.google.com/search?q=gmail+multiple+addresses&ie=utf-8&oe=utf-8
will give you lots of articles describing all the various aspects of using that Gmail feature.