Can I integrate Outlook with Yammer in such a way that people in my contacts (Outlook) can be directly added in a group on Yammer ?
Or can I forward a mail directly to a user on Yammer as a message?
Is it possible to create an application that allows me to exchange data between Yammer and Outlook?
What you are looking at seems totally possible for me. I believe the best approach would be to register your app with Azure AD. Both Yammer and Outlook REST APIs can be discovered with Azure AD, see this link for example.
So now that you know that you will target Azure AD with OAUTH flow. You have to ask yourself if you want your app to do the requests or your web server will do it (see OAUTH flow "implicit" vs "code authorization").