No, email is not included with the care plan.
Web hosting and email hosting, though they both mention hosting, are very different products, and just because a company is good at web hosting doesn’t mean they’re good at email.
There’s a number of very good reasons to separate your email from your web host– getting your emails actually delivered instead of landing in the “spam” folder or simply disappearing into the ether is the #1 benefit.
You can have a professional, branded email like yourname@example.com for a low monthly cost from a dedicated email vendor (usually between $1-6 USD depending on the features you want), and I can help set that up for you if you need to transition away from the freebie setup at your current host or set up a brand new account. After that, your email host will provide support. Believe me, it’s worth it to get your emails delivered and read!