1) The 'wallet' seems to be mis-named. As I understand it, it's a cryptographic ID and account number in one; but does not actually hold 'coins' within itself. Is this correct?
Yes. A 'wallet' might better be called a 'private bank' which is filled with many different account numbers, each of which contain a number of 'coins'.
2-5, what Red said.
And I *really* don't understand how change works.
You always have to spend all the money in an account (address) at once.
eg:
I have 10 BTC in Address1, I want to pay you 1 BTC.
TXin:
Address1: 10 BTC
TXout:
Address2: 1 BTC (this goes to you)
Address3: 9 BTC (this goes to me - the change)
Address1: is now empty.
A cool side-effect here is that anyone analyzing the transactions can't easily tell if I paid 1 BTC or 9 BTC. (assuming they know I have Address1, but don't know who has Address2 or Address3)