This is not a SFW instance. NSFW communities will be tagged, and efforts will be made to keep SFW communities clean, but proceed at your own comfort level.
The stay logged on and trust this system actions are probably controlled by a browser cookie, so won’t work if you don’t allow cookies from that site.
In my experience, they are. In my bowser, I have to explicitly allow the saving of site data if I hope to be able to keep myself logged in. For me, this is fine; I only want to stay logged in on a handful of sites anyway so the tradeoff between adding an exception for some sites vs. allowing every single site I visit to be able to save some piece of data doing god-knows-what (likely helping Facebook and the like track where it is I visit) on my machine is worth it.
In my experience, they are. In my bowser, I have to explicitly allow the saving of site data if I hope to be able to keep myself logged in. For me, this is fine; I only want to stay logged in on a handful of sites anyway so the tradeoff between adding an exception for some sites vs. allowing every single site I visit to be able to save some piece of data doing god-knows-what (likely helping Facebook and the like track where it is I visit) on my machine is worth it.