First go to admin -> configuration -> e-mail options and make sure you enable the options to receive copies of e-mails.

E-mails are generated/activated automatically by Zen Cart.

a. What e-mails will I get that are generated by the program (when a customer registers or places an order)? What activates them. What they mean. What do I do with them. etc.

b. Handling New Customers… What tells me someone is registered. How do I look at the Customer data. Can the Customer data be transferred to a stand-alone data base or is there now a way to print off this data? etc.
If you have configured your e-mail options correctly, you will receive a confirmation e-mail of new registrations.
Depending on what the customer was doing at the time the e-mail was generated, they mean someone created an account or placed an order.

After reading the e-mail you can do whatever you want with them.

Go to admin -> customer -> customers you will be presented with a list of customers which you can edit, delete, or send an e-mail.

You can use phpmyadmin to generate the customer data and then put it into a standalone database.

At present you cannot print the customer data but that may change when the admin portion of Zen Cart is re-written.

c. Processing Orders…. How do I know I got an order? What do I do next? How and what do I change in my ZC program as I process an order? etc.
If you have configured your e-mail options correctly, you will receive an order confirmation e-mail.
Fill the order and send it to the customer.
go to admin -> customers -> orders you will be presented with a list of orders which you can edit as necessary.

d. What about creating a Newsletter? How to generate a newsletter. How to send. etc.
Go to admin -> tools -> newsletter and product notification manager
click the new newsletter button
create your content
click the save button and follow the instructions from there.
The newsletter is generated and e-mailed automatically.