I have a router with a built-in firewall (the router box said that it has but I'm not sure how to configure it). I have done a research from the internet. I have found out that a router's built-in firewall only protects a computer from inbound connections. Is it still advisable to install a 3rd party firewall software like Comodo Personal Firewall Pro, since it scans inbound and outbound connections?

You bet it is. Here's a selection of three free..
ZoneAlarm Free, Kerio, Comodo

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