These are regarding Darkseid’s rocky history, considering his highs and lows as DC’s top villain.

1.)     Which appearances have Darkseid as an avatar?

2.)     For any of the losses that might not have avatars (Getting a piece of Wonder Woman’s soul inside him, losing to Doomsday), is their another explanation entirely for those losses?

3.)     How powerful was Darkseid before seizing the Omega Effect/Force from his older brother?

4.)     How does the possession of human bodies work for the New Gods? Is it different for each particular New God?

5.)     Is there a fine line seperating people who have legitimately outsmarted Darkseid and people who only made him look incompetent out of sheer PIS/CIS? Batman comes to mind for the latter.    

1.) Apparently Final Crisis retconned every version of him before Final Crisis as an avatar even though it also causes a lot of continuity issues.
2.) Some of his losses as the real Darkseid are PIS and writers knowing nothing about him. Thing is that he is a New Gods villain but some writers like Loeb didn't do much research on him at all and presumed he was a Superman villain and so they treated him like one.
3.) I'm not that sure. There were some appearances in Tales of the New Gods stories which appeared at the end of issues of Jack Kirby's Fourth World but not a whole lot of appearances.
4.) Not sure about this
5.) Not sure how to answer this one either.