First you need to grasp that unlike in Satoshi's design where we have one single longest chain rule as acceptance truth, in a DAG there are many competing chains vying to be truth and no globally enforced protocol rule to select between them. The DAG's truth is the payer's model of how payers select which transactions to reference in their transactions and a second acceptance model of how we calculate the probability that the first model will select a conflicting double-spend. Thus the security is never based on any particular deterministic chain in the graph, but rather on the models that the payers and payees are using to model the DAG.
Until you understand that, you understand nothing about a DAG.
Whether that is more powerful or less secure than Satoshi's design is what CfB and I are debating and discussing.
My point has been that each payer and payee can choose a different model so the game theory of the security is unfathomable. The white paper shows that under a given model, certain attacks are too costly. But the white paper can't show what happens under all game theories and thus can't present any holistic model of attack cost.
No, all heads that don't lead to conflicting ledger will merge. In case if it's not obvious, the number of heads is equal to the number of transactions. In ABCDEF sequence someone can still ignore "F" and pick "E" as a head. From the global point of view all heads will exist, "survives" doesn't make sense just like "orphaning". I find it very hard to explain the idea of Tangle, but once you get this idea you will see that if you send a double-spending right after the legit transaction you increase security of the tangle, not attack it. This is because you fight not only against the system but also against other attackers. "Enemy of my enemy is my friend" perfectly works here.
Piecemeal details like this will just cause the thread to become noisy because they won't help the reader gain understanding of the real way a DAG security works. Discussing the deterministic structure of the DAG is misleading discussion. We need to first explain the above as I did.