I was wondering if there is a way to make a list automatically email to an external users email when a new item is created/edited. I know users can set up alerts on lists, but this only works for their outlook emails. On a separate note, when you're setting up an alert, there is a text message option. This option is greyed out for me. Is there any way to change this?
To trigger an email, most people will tell you how to create a workflow (probably with SharePoint Designer). That's quite easy, it would work in most cases. But it's not the purpose of workflows (+ they do appear in the UI, they're slow, ...)
Another approach is to ask a developer to create a custom App (sorry we have to say "add-in" now). That app would contain a "remote event receiver", i.e. a Web service triggered when an item is added. That Web service would send the email.
About the Text Message option: it's grayed out because it's not configured (it can be configured with a texting service provider on on-prem installations). But I'm not sure it's available at all in SP online.
The easy answer, for now, is to make a SharePoint 2010 workflow in SPD and use that to send the email to an external email address since the 2010 version (unlike 2013 version) can send to external emails.