Do devices show up if you're using someone's Wi-Fi?

Scenario: Emily has an iPhone 5. If she types in the pass code for her parents' Wi-Fi, is there like a list of devices or something that they can look at and see the iPhone 5 is using their Wi-Fi?

Most routers record details of devices that have been connected to them over Ethernet or Wi-Fi, especially if a device is set to get its addresses automatically, which is the default. Home routers do not normally log the sites visited - they simply do not have the storage in them to record that level of information. Home router logs are there mainly for diagnosing problems with their operation and the network connections to the router (Ethernet, Wi-Fi and ISP). Many such routers have volatile storage, which is cleared down when the router is restarted, although some modern routers have flash memory for the logs, which preserves the information over a restart.

Accessing any network, including Ethernet and Wi-Fi, and even Wi-Fi that is not encrypted, is illegal if you do not have the network owner's explicit or implied permission. If you go into a coffee shop and buy something, then you will normally have implied permission to use their Wi-Fi during that particular visit. If you leave and come back later and use their Wi-Fi without buying something else, then you no longer have implied permission.

Without permission, you are guilty of theft and possibly hacking as well.

In your example, if Emily uses her parents' Wi-Fi, unless her parents have given her long term permission to do so then technically she is committing an offence although it is unlikely that any action would be taken directly against her.

Yeah, it's called inet

Yes.

Basically every router these days registers which devices are currently connected to it, and which have recently connected to it. It takes a browser and 10 seconds to find out.

Yes. All connected devices, and all previously connected devices and what sites they visited, are all recorded in the router logs.

Depending on their setup & apps available that scan the network, yes.

Dk

Yes, they have to the router you connect to or the modem hands out an IP address for the network, to do that it has to record the device identity usually the MAC address that uniquely identifies the device. The log is kept so that if it reconnects it can do so quickly, it may "forget" the device and give it a new number when you reconect but the main log will usually always say it connected.