When there is only one site then no host name mapping is needed all hosts names that come to the installation use the same single site. The only purpose of the host name mapping is for resolving the site id so if there is only 1 site there is no need to resolve anything.

In a multi site installation, the new site must first be saved before the host name can be added because the site id must be established, so the tab for host names is not shown in the ui until after the new site is first saved.

When you add a host name it is done inside an updatepanel which may in some cases be slow to update in the ui. I will look into preventing duplicates but you should be careful about it in the meantime to avoid any duplication, ultimately it will resolve to the first site id it finds attached to the host name.

For SEO you really do not want your site to use both the domain with and without www (nor do you want multiple domains with the same content), so you should pick one and force it as the preferred one.

I'm not clear from your question exactly what things you have configured

you should have host name mappings for www.domain.com and domain.com if you want the site to respond to both.

Then if you want the preferred to be without www then put domain.com for the preferred hostname

I have just the opposite on this site www.mojoportal.com is preferred so for example the url (whether entered manually or clicked) http://mojoportal.com/community will redirect to http://www.mojoportal.com/community it will not result in page not found

it should work no differently going the other way with and without www is just 2 host names

if one of yours is not working first make sure it is resolving to the correct ip address when you ping the host name and if it is a shared ip address with other sites then there must also be in IIS host name headers to make it resolve to the correct IIS site. I'm not sure how that plays out in Azure but if you get an IIS 404 page then it is not even reaching mojoPortal code