Yes. In Thunderdome, a combatant must kill his opponent to win hence "Two men enter. One man leaves". Max breaks this when he refuses to kill Blaster and fulfill his part of the deal with Aunty Entity. The "no rules" means that there's no specific restrictions on how one is able to defeat their opponent.
Max, a warrior arrives in Bartertown, a desert town where people come to trade and do business. Max has come to Bartertown as he is tracking down an eccentric pilot whom hijacked his vehicle and stole all his possessions. In Bartertown, Max is brought before Aunty Entity, the town's tyrannical ruler and Aunty Entity impressed with Max's skills hires him as an assassin to kill Blaster, an enigmatic masked giant whom helps an intelligent dwarf called Master whom runs the power station behind Bartertown. After he fights Blaster in a gladiatorial arena called Bartertown, Max is banished and sent out into the desert to die when he refuses to kill Blaster upon learning he is mentally disabled. In the desert, Max is found and nursed back to health by a tribe of children led by a teenage girl called Savannah. Max learns that the tribe were the survivors of a crashed airplane and they mistook Max for their the pilot Captain Walker and that he has returned to take him to their promised land Tomorrow-Morrow Land. When Savannah and some of the children leave and set out on foot in search of Tomorrow-Morrow Land, Max and some other children goes after them which they soon reach Bartertown and Max decides to go back to Bartertown and decides to settle a score with Aunty Entity.
Yes! Out at the Burning Man Festival, there is a camp called Deathguild that builds its own Road Warrior style cars and holds nightly battles in its own Thunderdome!
They were the descendants of Captain Walker and the surviving crew and passengers of the passenger jet that Walker piloted. The story they tell about the apocalypse and Walker's crash landing in the desert is one that's been handed down through their time living in the canyon. When Savannah (who herself is pregnant) finds Max, she assumes that he's Captain Walker and that he's returned to lead them out of the desert to civilization. Years prior to Max' arrival, Walker and maybe a few of his crew and some of the passengers probably trekked into the desert to find a way back to civilization. The fact that they never returned may mean that they died out there.
No, Bruce Spence plays a different character. Although both are pilots, the Gyro Captain from Mad Max 2 was said to become the leader of the survivor group from that film. Then the narrator of MM2 mentions that when he grew up, he eventually took over the group. So it stands to reason that the Gyro Captain would not be found in Barter Town if he was still leading a group at that time. Also, Max and Jedediah (the character from this film) see each other on more than one occasion and never have a moment where they recognize each other.
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