Answers to your questions below

As far as I can tell I put the product details in the parent listing and then that auto-populates to all child listings. Is this correct?

Its supposed to work this way but I always end up putting unique product details on all the childs anyway because some problem always occurs.

If the above is yes, what do I put for the title since it is the parent and not the child? I have used the basic description without the design variation. As I understand this Parent is never shown in the store. Is that correct?

Sometimes, the parent title is the only thing you can add...which populates to all of the child ASINS. I would recommend adding a generic title that applies to all variations and the listing will automatically add a variation tag at the end of the title.

Example title here (Variation1)

Do I then go into every variation and add the design name to the overall title?

This happens many times. You can also go into the child ASINS and edit every title if you choose to do so.

I added product description and 5 separate key product features. Only the description is showing up. Any idea why that would be?

Try going into each child and adding the key product features.

The description shows up as one paragraph - even though I have breaks in the copy. I will search to see if I can figure that out but thought I would put it here as well.

You mentioned you have A+ content capabilities. Once you add A+ content, your description is not visible anyway.

My main concern is the listing (which is far from being done) is showing "live" but out of stock. Is this normal? I assumed I was working in an unpublished draft but when I click the title it takes me to the amazon page with an out-of-stock listing. (I am in the process of getting my first shipment to Amazon) Have I hit the wrong thing and messed this up?

No one will see it as long as its out of stock. Once its in stock, it will be visible but its unlikely anyone will see it without advertisements.