Email Fundamentals (broken)

I've been using email for about 25 years now, and now find myself working with an organization that seems to not understand some email fundamentals.

Everyone NEEDS their own email address if they use email professionally, and everyone needs to sign their own emails. This is soooo obvious to my readers I'm not quite sure why I'm writing it - clearly it isn't obvious to everyone.

This small organization has a director and a coordinator. They share an email. Apparently they don't have other email addresses; so they tell me. The director has more experience and some questions require her expertise. The coordinator usually answers emails. The director says she reads every single email.

Of course, emails get lost, from my direct experience quite often. Or at least they go unanswered. No surprise.

Usually the coordinator signs her emails with her name, sometimes she doesn't. Her emails are somewhat obvious as she sends a lot of emails and her responses tend to be short one or two liners which are direct and to the point.
The director's emails seem to get signed with the coordinators name as well. Her emails tend to stand out as they are much longer and heartfelt.
Once I got an email signed by someone I didn't know worked in the office - still not sure who she is? Part-timer? Temp?
An occasional email is written by both - signed by the coordinator of course. Hmm, maybe once both names were signed.

And the shocker - They PREFER to communicate by email!

So, what's wrong here? Briefly:
1) When an email is received, its hard to know who it came from.

2) When you send an email, its hard to know who reads it.

3) Emails *always* get lost in scenarios like this. Certainly they are in this case.

4) From the customer service viewpoint, one person needs to be in charge of each customer request/question/issue. It's hard to tell what is happening here.

They should teach this stuff in school! Not everyone has been using email as long as myself - maybe it's not all obvious??