Use an onion browser like "Tor" with "Whonix" if you want a decent level of anonymity.
The mac address is accessible via your browser to get around your router masking the machines mac address to the next node. Someone looking for your address will exploit your commercial browser and make a few commands on your PC to establish the mac address.
Given the various security agencies around the world demand certain backdoors to software, it's no inconceivable they get a free pass via a non disclosed transport layer.
Otherwise take heed of your mum's words about not saying anything you don't want the whole world to hear. Sedition is a moving feast that has a wide interpretation.
