Upcoming change:Updating default sharing setting for Office 365 Group connected SPO site collections

My question is really about the differences between needing to have someone in the organization directory, and authenticated external users. Currently, we set our external sharing site collections to authenticated external users indicating they either work for our company and have their email address, or they are an extenal user who needs to set up a Microsoft Account if they do not already have one that they are using with the email address. We have found that recently, external users are having issues accepting invites to external sharing site collections if they are not already in our directory--not sure how they got into our directory in the first place since we did not add them.

1. Was that automatic when they signed up for the free Microsoft Live account and accepted the invite?

2. If you set the option for users in the Organization Directory, who adds them? The tenant admin?

3. Why would external users not be able to accept invitations to site collections if they sign up for the free account--but are no listed in our Organizational Directory?