It was complex, and it was difficult; but I was able to get a hybrid setup with my exchange server (on-premises) with Office 365

I am still working on other items such as logging in with a default domain suffix of my choosing but more on that later.

The issue I had faced involved sending emails from my email account now hosted in O365 to emails on my On-Premise Exchange Server. Each attempt would fail.

So I followed the steps listed in the following kb article  kb2730609

  1. Sign in to the Office 365 portal (https://portal.microsoftonline.com) as a global admin.
  2. In the header, click Admin, and then click Exchange.
  3. In the left navigation pane of the Exchange Admin Center, click Mail Flow, and then click Accepted Domains.
  4. Select the domain that is set up for the hybrid deployment, and then click Details.
  5. Select Shared, and then click Save.

As I said prior somethings were complex and I will address that as this was only part of my resolution