I would like to create a firewall rule which prevents users in the LAN to communicate directly with other users. In other words, deny access from any LAN address to all other LAN addresses. Is this possible to achieve? The router is DIR-815.
I think it's possible, but you'll need to install dd-wrt so you can edit the routing table to put in purposefully-broken routes for your local subnet. It's also depends on how the ports on the router are set up. If the LAN ports are just a dumb hub, then every transmission is seen by every client and there will be nothing you can do to stop this. You're hoping for real switched ports.