Say the agent is running under user alice, and the flows are being registered by user bob. Into whose home directory does ~/.prefect/config.toml belong?

Assuming you're talking about a local agent, the config directory that affects the agent is the one that will affect runtime behavior of flow runs. The config for the user registering flows only affects registration-time options.

Does the agent need to be restarted to pick up changes to its config.toml?

Yes, those are loaded on init only.

Is there a complete list of config file options available?

There is not (it's an open issue). The existing config file has most of the common ones present and commented: https://github.com/PrefectHQ/prefect/blob/master/src/prefect/config.toml

Not really. Studying logging at the moment, and I see a few options in config.toml you referenced above.

yes