Once dhcpd (IPv4) is started, is there any way to check its internal pool status? e.g how many addresses are available?
I checked man(8) dhcpd, there's no signals/files available for that info.
Checking status of leases is easiest with analysis tool.
http://dhcpd-pools.sourceforge.net/
After building the dhcpd-pools, you can use dhcpd.conf and dhcpd.leases as inputs to the command ./dhcpd-pools.
On Ubuntu there is the file /var/lib/dhcp/dhcpd.leases, but it is rather verbose and you probably need a little script if you want more high level statistics. I am unaware of existing tools to do this.
There is a separate man page for this file man dhcpd.leases describing the database format.
/var/state/dhcp/dhcpd.leases
lease-file-name in dhcpd.conf IIRC.