Yes, if you intend to connect to the Internet and use email, the World Wide Web and other Internet-based services.
Unfortunately, no. A firewall, whether it is built-in or separate to the router, must be properly configured by professionals to ensure your router is secure. Even after this is done there are still other attack vectors open to criminals that firewalls may not stop.
A critical part of ensuring a router is secure is keeping the firmware up to date. Firmware is the device-specific software that controls how the router works. Firmware can be flawed and present security holes to hackers – when these flaws are discovered, the manufacturer will release an update which should be enacted promptly.
Unfortunately, no. Updating firmware can cause problems itself due to technical issues. From time to time, firewalls my cause problems by blocking legitimate access to and from your network. In either situation, this can lead to downtime required to fix the problems. Whenever you are considering any kind of router maintenance, make a contingency plan in the event of any problems, and take a backup of the router configuration in case you need to restore it to a previous working state.