Users control what sites they want to allow it to record so no privacy worries, especially assuming the plugin is open source.
No automated crawling. The plugin does not drive the users browser to fetch things. Just whatever a user happens to actually view on their own, some percentage of those views from the activated domains gets submitted up to some archive.
Not every view, just like maybe 100 people each submit 1% of views, and maybe it's a random selection or maybe it's weighted by some feedback mechanism where the archive destination can say "Hey if the user views this particular url, I still don't have that one yet so definitely send that one if you see it rather than just applying the normal random chance"
Not sure how to protect the archive itself or it's operators.