These settings apply only when clients use router’s own address as DNS resolver.
If your clients use some external resolver, these settings will not influence them in any way.
If you do not check Allow Remote Requests, router will resolve names only for itself (e.g. when you have hostname in its VPN client, etc..). If you do check it, router will act as resolver for any other machine that asks for it.
Unfortunately there’s no option to allow just LAN clients (there’s a feature request, but who knows if it ever gets implemented). So when you enable Allow Remote Requests, you have to make sure that you allow incoming port 53 only for your clients and block the rest of the world using firewall. Otherwise you’ll create open resolver and it’s a bad thing.