Firewall (ESS for that matter)

I know nothing about network, nor do i know about computing, but i'd like to start learning.

The firewall must connect to the internet after booting to check for software updates... and I don't know what else. depends what the manufacturer desires.

first question is: what information can they get if I allow connections in firewall?
Lets assume the only program that is connected to the internet is my firewall, how can I monitor what it sends out and receive?
I don't want to be traced.
will wireshark help me do it?

2. Sometimes I get a pop up from my firewall telling me whether to allow or deny.
what happens when I click allow?