External stones in tsumegos

This situation came up during a game, where I was playing Black against Mr. Mk a few days ago, after a 3-3 invasion. Due to the presence of the B and C stones, his invasion wasn't too big, but the correct timing made of it the biggest move on board.

You may already be familiar with this shape. You may say that the vital point is D. I did too, but I was unaware of the relevancy of the stones around E and F.
During the game I played D as a ko threat because I knew I couldn't kill white but forced his response, white answered and we moved on with the ko. Later, during the yose and already in byo-yomi, we realised that the group was dead. Why?

Can you kill white by just placing a stone at D?
Can you kill white if you already had a stone at E?
Can you kill white if you already had a stone at F?

You have this simple tsumego loaded on Zgo on the "continue reading section".

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