Oh, goodness no. Anonymity on the internet is a pipe dream and anyone who thinks they can remain anonymous is very naive. I would say that FR is under more scrutiny than most realize so sometimes it is better to tread softly but wear steeltoed shoes.
Yep, especially if you pay for an internet connection.
BUT one can use the Internet a be anonymous but the commitment to do so is akin to a wanted felon trying to stay off the grid.
It would require constant travel and constant switching to new laptops/tablets that are bought used and not registered while avoiding surveillance cameras (while using public wifi which more and more have cameras trained on the reception area) and any use of any form of payment that can be tracked to your name. IOW nearly impossible.