Hey all I was just wondering when a Paradox Generator is used, does the conformation box appear that comes up when selling ship mods or using an Annex Decree that goes something like "Are you sure you want to Use/Sell 'Insert Artifact/Ship Mod Here'?"

yes, they do

Do they work during New Year? If so, is it worth it to burn at least 5 to have spheres for future race changes?

That's a matter of opinion. I plan to utilize mine in such a way that I can get some nice planets i have on scan which I wouldn't stand a chance on otherwise (As they'd get fluxed), AND get the spheres of the New Era. (Yes, they do work on New Years's- I did that before I reset)

yeah, this is best. do a scan run right before new year, prep your invasion artifacts(like the sacs) and charge!