A row in the ARP table (IP to MAC translation) of a router is only automatically created when a packet needs to be delivered to a host whose IP is in a connected subnet. So until you try to ping that IP, or some packet for it comes from outside, the ARP record will never appear automatically. This is a difference as compared to MAC forwarding table of a switch/bridge, where the mapping between a MAC address and an interface is created whenever a frame from that MAC address arrives via that interface.
In both tables, dynamically created rows have a lifetime - if there is no update before the lifetime expires, the row is automatically removed.
To both tables, you can add a row manually; such rows are stored into the configuration so they survive a reboot.
You can configure the DHCP server to create an ARP record once it leases out the address to a client, and remove it when the lease expires. Nothing similar exists for MAC table for switches/bridges.
Instead of writing novels, post /export hide-sensitive. Use find&replace in your favourite text editor to systematically replace all occurrences of each public IP address potentially identifying you by a distinctive pattern such as my.public.ip.1.