Question: Does a force at a friendly base or planet have a requirement to accept an approach battle if an enemy uses fighting retreat to enter the hex?

Answer: No, they do not have the accept the approach battle (no one ever does) and the fighting retreat forces will then just keep retreating. In effect, the forces at the planet decided not to block the retreat.

Question: Rule (323.51) states: "If neither player retreats [either as retreat action (323.32) or normally under (302.7)], continue using the ESSC system for additional rounds if necessary. If one player retreats and the other player elects to pursue, then follow the procedures for pursuit (307.0) normally but use these ESSC procedures for resolving any pursuit combat."

Now it makes perfect sense that in the Pursuit Round, a casualty could not be resolved by using retreat again because one side is already fleeing and other side gave up the option to give chase. But, this is nowhere stated or explained in the new rule. So is it the case that a casualty can not be resolved as a retreat if it is a pursuit round?

Answer: I asked Chuck Strong (who wrote the rule) and he replied: Since there is no option to retreat during a pursuit round, the player suffering a casualty cannot take the "retreat" option and must resolve the casualty on a valid unit.

Question: I have a fleet of ships that is retreating. There is no hex that will be in supply from the main supply grid after the retreat. There is also no neutral hexes adjacent to the fleet, nor do any of the six hexes contain more ships than the retreating fleet. There is one hex that can be supplied by a partial supply grid after the retreat, but when the fleet started the turn it was in supply from the main supply grid, so partial supply grid costs were not paid. The question: Is my fleet of ships required to retreat toward the partial supply grid, or may they retreat into any of the six adjacent hexes?

Answer: (302.733) Step 3: Sub-Step-C only allows you to ignore a partial supply grid if there is a retreat hex in the main grid. In your example, there is no retreat hex that is connected to the main grid, so Sub-Step-B remains in effect and you have to retreat towards supply, i.e., toward the partial grid.