Can the master broodwalker move 6 spaces each turn, since it has 2 natural move (*2 actions) and gets 2 move points at the start of each of its activations?

When it dies, I assume the overlord can reinforce it as normal as one "broodwalker"?

Does this mean it can effectively go to the Hive on 2 turns as long as it is alive an unhindered in any way?

Does that in turn mean that the heroes wants to, for sure, kill it asap all the time so they won't die to the Hive ability each round once it's on the Hive?

Yes, all statement correct.

I have not played that quest myself, but yes, I guess preventing the master broodwalker to reach the hive should be high priority for the heroes.