The friend of my mother says he could check my online time via the ID of my notebook. Is that really, or is he bluffing?
Yes does not mean id but up or MAC address
You can already see how long a device is connected to the router (which conjures up the Wi-Fi).
Apart from that, there are definitely reporting tools on the computer depending on the model.
Yes, according to router with the ip / mac address already.
Which ID?
IP address? MAC address? Serial number?
Anyway, no, he can't if he is not just friends with your various accounts (Steam, Uplay, Epic, …) and count.
EDIT
I read it, yes he can look at the router when your PC is online, based on the MAC address.