I myself (having used Outlook 2007) don't know enough about these things to know whether it might be something about your recipients' mail settings or not. But if you're able to send an email successfully to yourself with the image showing inline, it might mean that something about your version of Outlook (what version is it, btw? 2003? 2007? 2010?) is triggering the removal of the image from the body of the message. But I would think if that were the case, then your recipients would at least get the notification "some images have been removed for your safety; click here to display them." Incidentally, you said you sent the test emails to yourself. I take it you viewed those messages in your offline client (Outlook). Did you also view them in your webmail to see if they displayed inline there as well? As another resource, you might want to check the Outlook forums here. I've used them in the past and have gotten good help. I did a quick search there for your issue and found two from 2010 here and here. In neither case did the OP continue the thread, so I have no idea if anything was resolved, but the answers didn't seem to encouraging. :-( But if your version of Outlook is more recent than those available at the time, there may be different settings to try, so you may wish to inquire there anyway. ???

How about trying this: In the Upper Left Corner of Outlook.com there is a Square with 9 Smaller Squares in it, click on it. Chose Word Online and Type your document for there! There is a Print Icon in the Tool Bar over towards the left or you could chose File on the Tool Bar to the Right and chose Print form the list! Hopefully you have this option on your computer and it's not just something I have! I have Either Office 2007 Professional or Business on this Laptop and my wife's has the other. On my Tablet I have Office 2013 Home and Student and then on my Phone I have ? but it has Word, Excel, OneNote, OneDrive and maybe something else. Maybe one of those Office packages has installed this Icon and given me access to these programs online, I'm not sure. If you have it, give it a try, it may be much easier for you! BTW, I know I don't have Office 365 on any of my devices!

Click "New Email" as if you are going to compose an email. At the top of the new email is a "Signatures" tab. Click that and it will let you add a permanent signature.

You can mark individual emails as "not junk." That will move them back to your inbox, and Outlook will not send emails from that sender to your junk box again.