I'm a little confused about what you are asking. You have cable coming into your house/apartment/condo and you've attached a router to it so that multiple systems can access the cable modem? You then need to instruct ZoneAlarm to allow inbound traffic from the router to your system?
So your setup (typical) would look something like this:
Internet------cable(modem)--------router---------home computers
I'm not real familiar with how ZoneAlarm works in terms of the interface or why you need to allow access from the router, however I can comment on the IP address concern.
There are several classes and two "types" of IP addresses. We really are only concerned with the later. IP address are either privatve (non-routable) or public (routable). Public IP addresses are unique on the internet. No two systems can exist on the network with the same IP address. This presents a problem because the current scheme only allows 2^32 addresses. To fix this little problem private IP addresses were created. These addresses are not unique to a system and many hosts can have the same private IP address. A system with a private IP can not connect directly to the internet. What happens is the router takes your private IP and translates it to your public IP address (this is called NAT: Network Address Translation) that the cable company has assigned to your router. This is how you can have many machines on your home network connect to the internet using the same connection because there are hundreds of thousands maybe millions of machines connected to the internet in this manner. Your IP private default address isn't the concern. And also what may be happening is your cable provider is giving you a private IP which they are translating to a public IP. So your data must translate twice before it makes it's way on to the internet. Your default private IP isn't the issue.
What is a concern is the password assigned to that router and any exploits the router software has. If the router has a weak password then you might have a problem provided the attacker can side step your cable provider's defenses to get to you.
The trick to home system security is to make getting into your system hard enough that the time and effort aren't warranted.
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