As it says on the tin, can a wizard copy one of the new spells from this artifact into his spellbook?
I don't see why not, it can be used as a scroll, and you can copy spells from the scrolls.
I think so, though they still have to worry about the side effects of the artifact.
As far as I can tell, it's only useful for copying one of the seven Thassilonian "sin" spells.
All the other spells that it can present are those arcane spells which the caster already "knows how to cast", i.e., spells already in the caster's spellbook (or spells known in the case of a spontaneous caster). That means that, aside from the aforementioned sin spells, it's only good as an "emergency scroll" based on one's own spellbook (with an increasingly risky side-effect).
The same dangers also apply to using it as a research aid.
It's also good for casting spells with expensive material components or foci. Since casting them from the Anathema Archive is like casting from a scroll, no material component of focus is required.
Yes, this eventually means a free wish every day with an increasingly irrelevant side effect. I'm beefing up the badness for my game by increasing the side effect each time it occurs rather than just increasing the DC each time it's used.
...Yes, this eventually means a free wish every day with an increasingly irrelevant side effect.
I'd agree with this. The wisdom drain can be easily overcome with a Restoration spell and the confusion lasts only rounds. All the penalties do is discourage use of the Archive in combat. There are a good number of utility spells that are cheaply available beside Wish - Limited Wish, Permanency, Planar Binding (all flavors) etc.
So amusingly my players have become too spooked to use this a second time. First use it gave them Sign of Wrath, which was copied into a spellbook, but the will save for unknown reasons afterward is causing them to now ignore this item.