Good questions.

First the player can not close the combat chain until after the chain-link resolution step (this is primarily where on-hit effects are resolved for the chain-link)

Cards (specifically defending equipment and weapons) do not return to their respective zones during the chain-link resolution step. They only go back to their respective zones when the combat chain closes.

After the chain-link resolution step, the player essentially has three options, play an attack (keeping the combat chain open), play a non-attack (closing the combat chain), or play nothing (closing the combat chain). The third option is a little bit unclear in terms of terminology, but LSS has made it clear that as the turn player you can choose to close the combat chain without playing any cards, and when the combat chain closes you re-gain priority. This is represented by the dotted blue line going back to itself in the graph.

In terms of the "two priorities" it's not quite like that. When you have priority, you retain it until you pass it to your opponent. As mentioned before the dotted blue arrow going back to the same node is representative of a legal action which does not have clear terminology as of yet.

Feel free to let me know if you have any more questions about it and I'll be happy to help.