Microsoft Apps for Business 365 w/o Microsoft Exchange / Email

Question

Recently, I moved a very small team (2 people) to using Microsoft Business Apps - which is basically office 365 & OneDrive.

This team already have external email which they are not interested in moving. This is why I picked the product of Microsoft Business Apps as it does not include any exchange or email services.

Set up was very simple and move worked at first what felt as without any issues.

However, when it comes to sharing to and from the members of this team either between each other or with any outside users; this doesn't work.

It can work using the links; however, the problem is that according to Microsoft from the outside of the tenant; the users do not exist. And from inside the tenant; they can share with anyone; but no emails go out.

So, besides the onmicrosoft domain, I used the customer's actual email domain.

Should I have used the onmicrosoft account and will that route / send emails to their domain?

Has anyone had this issue and what is the solution here. What is the best path forward. Besides moving their email to Microsoft.

Is there a way to just MX out the email and let Microsoft handle the office / onedrive stuff?

Why does the Business Apps product even exist if you cannot use external email?

Thanks for any help or direction?

Thanks,
TZ