Do you regularly leave your house and leave all the doors unlocked?
In some parts of the country you might still do that, but most people would still agree it's a bad idea, and many others would agree that it's your fault if someone walked in through your open door and trashed your house.
The same goes for a computer without a firewall.
The short answer is you should ALWAYS use a firewall, especially if you have one and there's no cost to using it.
Turn on your firewall and block ALL incoming traffic except the ports required for the web server and traffic initiated from the inside.
Without seeing the specific log messages you're referring to, it's impossible to predict what they might be, and if they're http requests to your server, turning on your firewall won't stop them, but (to use the house analogy) at least you're only letting people look at your front garden instead of letting them wander around the house.
In some parts of the country you might still do that, but most people would still agree it's a bad idea, and many others would agree that it's your fault if someone walked in through your open door and trashed your house.
The same goes for a computer without a firewall.
The short answer is you should ALWAYS use a firewall, especially if you have one and there's no cost to using it.
Turn on your firewall and block ALL incoming traffic except the ports required for the web server and traffic initiated from the inside.
Without seeing the specific log messages you're referring to, it's impossible to predict what they might be, and if they're http requests to your server, turning on your firewall won't stop them, but (to use the house analogy) at least you're only letting people look at your front garden instead of letting them wander around the house.