Thank you for the support and thorough comments, Sam!
1. Yes, deterministic/nondeterministic is more of a distinction when it comes to the key generation rather than the "type" of wallet. This is how it was conveyed in the Mastering Ethereum book, but I can see how it can be confusing because some people might take "type" to represent form factor (mobile/desktop/hardware). I'll update the section title to be Types of Key Generation
2. The MetaMask article mentions that as soon as a transaction is sent to an ethereum node, it enters a "local" mempool, which then gets picked up by the closest node in the network and propagated further: https://metamask.zendesk.com/hc/en-us/articles/4410741657499-User-Guide-Transactions