Yes I'm pretty sure the firewall icon has always been there.

By the way, i left the computer by itself for about an hour and i came back and it said it had a fair connection but then disappeared.

I might be able to find out what modem/router it is but i'm not sure how to find it. Am I able to look for it on the computer or do I physically have to look for it?

And I changed the listening port number thing and it didnt do anything.