Not the OP, but I'm a former AppleCare AHA (Tier 2).

Why do you guys book customers appointments when we can not service their device? (I.e. Vintage)

There's no reason this should happen except incompetency.

Why do you frequently make them appointments with your own name?

AppleCare reps can set up store appointments under customer's names using their logging software. The only reason I can think of any rep would ever set it up under their own name aside from making a mistake (and they shouldn't do it, but this is the only reason I can think of why they would) is if there's a problem setting up an appointment in the logging app they use, so they go to the service website using their own Apple ID to schedule the customer's appointment. (What they should do if they can't schedule an appointment directly from their logging app is direct the customer to the support website to do it themselves.)

Why do you tell them to just "walk in" when there are no appointments available?

I assure you this is pure negligence; I was repeatedly trained and informed to avoid sending customers to the store if at all possible due to stores already being overwhelmed, and to always schedule an appointment for the customer if they really want to go. If the customer decided not to make an appointment and just walk in, I always informed them that people with reservations have priority and there's no guarantee the store will be able to see them.

Why do many apple care agents book appointments for iPods when they have a Mac?

It's been a while, but if I recall, the logging app AppleCare reps use lets them choose what product to make an appointment for, and I think "iPod" might just be the default option. Of course, it's their responsibility to change it. I think many AppleCare reps don't know that the store has different Geniuses trained for different products, and that not picking the right product here throws everything off for you guys.

Have you ever been offered the opportunity to work in a store to better understand the full experience? Can you work in a store temporarily to better understand the full experience?

There is a store rotation program offered, at least for AHAs, to work in a local store for a while (usually around late summer and during the holidays). It's pitched to employees explicitly to give them a chance to better understand how the stores work.