how to monitor the device behind the router via snmp?
You can setup a vpn.
How i do it (without vpn)
Dns : *.somename.net
Host 1 : CR1.somename.net port 161
Host 2 : SW1.somename.net port (example) 1610
Host 3 : AP1.somename.net port (example) 1611
Etc etc
U need to portforward the ports to the devices (static/bind ip) and ofc acl 
If u use hostnames all the same u need to set hostname diplicate to true.
And over internet… Maybe u whant to use snmp v3 for encription.
cheers,
Roy