Module script behaviour when required by ID?

I'm just curious about some of the behaviours of module scripts when you require them by ID from the Roblox website.

Do they still return the same result for every subsequent call by require on the same network, or will they run again and return a different result?

If you update your module with new source code on the roblox website while a server is running, will every subsequent call by require use the updated module?

Lastly, can module scripts access their hierarchy when stored as a model on the roblox website? For example, if the module script is named "MainModule" and one of its children is a model called "Rocket", could it reference that model via script.Rocket?