So I have a Chase MPE and I remember that when I added an AU to my account, I just had to enter the AU's name; no SSN or other details required.
The AU card also has exactly the same card number, expiry and security code as my own (only the name is different). For all intents and purposes, it seems that Chase treats it as 'one account', including the earning of rewards. I suspect that if either myself or the AU were to misplace our MPE card, both cards will have to be re-issued.

Now I also have an Amex Hilton card, and Amex asks for the SSN of the AU, and states that a separate monthly statement will be generated, and from what it appears, a different card with different card number will be issued for the AU. My question then is, how will the rewards earning for the AU card be managed? Will it only accrue to a separate HHonors account belonging to the AU? And I am guessing that the AU's credit report will start showing this Amex Hilton account?

I vaguely remember Chase mentioning (when I was adding AU to the MPE) that the account will show up under the AU's credit report too. But I can't fathom how they'd get that done without the AU's SSN to begin with.

And yet, it is absolutely true. Through some sort of near-magical process, the bureaus guess and usually get it right.

There will be a card with a different number. (Which can also be used to double-dip on a single account for e.g. Amex Twitter sync promotions - long may it live...) Rewards will accrue to the original HHonors account.

My wife is AU on my discover IT card since 2011. I switched my discover cash back card to IT in may 2013. She can see the discover card listed in her credit report. Can she still apply for her own new discover IT card or might get denied because she has one in her name?

I do not have experience with discovery, but am AUs on many cards for my spouse with Citi, Amex, Chase, etc. This has not prevented me from getting the same card, so suspect the answer is the same.

I added my German Shepherd as an AU on my Citi Amex a few years back. Shortly thereafter she started getting pre-approved card offers in the mail. She must have a credit history of some type, but I have no idea if I could pull a credit report without a SSN. I always wanted to teach her to put her credit card on the counter at the vet to pay her own bill, but my vet doesn't take Amex.

She can definitely apply for her own Discover IT card.
A person is allowed to have a max of 2 discover cards as the main cardholder.

...quite the dog, if that's the only flaw in the plan...

How is that legal? I thought AU's had to be at least 13 years old. Pretty sure they mean Earth years, not dog years.

Each lender has their orn rules re card numbers. Amex issues a unique number for each card on the account, others lenders may or may not. If one person on the account has a lost or stolen card only that card needs to be replaced, and transaction and fraud patterns are developed at the person/card level vs the account level.