What's the architecture for this inside a network? Does each node have to have its own Bitcoin wallet, or can you have a central node on a network store all the bitcoins?
every node have it's own "wallet". each wallet consist of public/private keys, where public key is address.
So there is no centralized place where all wallets or coins stored. In fact, there is no coins - there is amounts assigned to each address (public key). And the whole bitcoin network is huge transactions book.