I just bought a 2017 Macbook Pro with the latest OS (Mojave). In the OS X Mojave Security and Privacy-Firewall settings, I set Firewall to "Block all incoming connections" as I am extra cautious, but will my software (such as Chrome web browser, Firefox, etc.) still get new updates? For example, will my Firefox browser still get the latest software updates or will I have to manually check for software updates because the firewall is blocking all incoming connections?
Those will not be blocked. Connections initiated from the outside ('the internet') will be blocked. However, connections initiated by your Macbook (like a check for software updates or just opening a website) will be allowed by the firewall.