[mothered]

Say for example you visit my house and yet there is no mobile reception but I have WiFi.
Do you connect to it and use Tor etc? If so, what do you use in order to stay anonymous and have privacy when the network is not configured to your liking?

It's (predominantly) what you do with the connection that's of concern.

Connect to It with your PC that's preconfigured with all privacy and anonymity settings In place.

Also would you say I have already compromised myself by using this forum without proper steps taken from the beginning?

In terms of this board per se, you're fine.