Sometimes; I've seen it called client isolation or something like that. Or, yeah, if you can get under the hood it's probably as easy as one or two iptables rules (or nftables or whatever).
Is this true? For devices on the same subnet, I'm petty sure they don't even have to takl to the router. Maybe a managed switch can stop it, but I doubt most home routers have anything more than a dumb switch in them.
It depends™:) Yeah, if you have a dumb switch with devices plugged in, then the upstream router probably isn't relevant. But if you've got all devices on wifi running through a single box that's a router+switch+WAP+modem (very common in consumer home networking) then that single network box is in an excellent position to control devices talking to each other. YMMV.
Client isolation is a Wi-Fi feature, not an Ethernet feature. So a wireless client can't talk directly to another wireless client when client isolation is on.