First, you have to understand what an IP address is.
IPs are not users. IPs are not accounts. IPs are the network address of the device that connects you to the internet.
This can be a home router, or a phone using mobile data, or a hub serving a whole local network (school, company, etc). Depending on your device, the way it connects to the internet, and the plan with your internet provider, your IP address can change several times a day, or every few weeks or months, or almost never.
This means if you block an IP and you're lucky, you will block a certain user for a while. However, if the IP address belongs to an internet cafe where the given user was using the free WLAN, then you block everyone using that internet cafe's WLAN.
So blocking an IP address can block a single user, or their home network, or a whole company or school. That's why IP-blocks should always be issued for a short time only and never infinitely.
Fandom staff can IP block.
Admins can IP block anonymous (unregistered or not logged-in) users.
There is an auto-block option that blocks accounts that try to login from the same IP the blocked account had when being blocked for 24 hours (to prevent just creating a new account after being blocked).