If the angels in perfect harmony with God could sin and fall, how can we be sure this won't happen to us sometime in eternity? If it's at all possible, eternity is long enough that it is bound to happen at some point.

Yes, if it's at all possible, eternity is long enough that it is bound to happen. And so it's good, I think, to know that it will not happen.

I do not have an answer to why God would permit Lucifer, an angel, to fall. In other words: How can a perfectly pure being with no evil inclinations suddenly have an evil inclination? And the answer is: I don't know. The most ultimate mystery to me is the origin of sin in created beings.

I will say God oversaw it and ultimately ordained it without himself culpably causing it. Culpably causing it. How you could cause it any other way, I'm not sure! And yet God reigns and ordains from before the Fall that there would be a crucified Savior for sinners. Therefore, it was all in the plan.

I don't know about the origin of sin, but us I know about, because the Bible talks about us.

"He who began a good work in you will complete it" (Philippians 1:6). If you have eternal life, it is eternal life! It's eternal life. He gave us eternal life. It's not 8 billion year life. It's eternal life: it lasts forever: "Nobody can pluck them out of my hand."

So the doctrine of perseverance in the New Testament is the doctrine that assures us that that work of perseverance in us lasts forever.

"I know my own, I make them mine, I chose them, they follow me, and nobody—not themselves or anybody—can pluck them out of my hand" (John 10:27-28).