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No, there is no Power Rangers museum anywhere in the world however Power Rangers originates from a Japanese series which is known by fans as Sentai or "Super Sentai" and while Sentai itself does not have a museum Toei does lend their Sentai belongings over to the museum (the museum is a Bandai museum) for display purposes. Some items that the Bandai Museum displays from the Sentai series include the zord suits, the zord models, Ranger suits and Monster suits.
There is no season that is called Power Rangers Pirate Armada however Power Rangers Super Megaforce features suits and zords that are pirate-themed.
The episode during Power Rangers Zeo in which the Mighty Morphin Power Rangers' suits are taken control of is the episode that is titled "King For a Day, Part 1" however only Tommy's previous White Ranger suit is taken control of and the suit was only taken control of within a dream.
Power rangers?
No, the Producers didn't usually let them keep anything from Power Rangers but especially their Power Rangers suits however there were some exceptions to this. Both Blake Foster and Jessica Rey were allowed to keep their Ranger suit and Alison MacInnis was allowed to keep her Lightspeed Rescue jacket.
The Power Rangers teams themselves do keep their zords as long as they are in use and are not currently using a new source of power however the team that produces the show, they do not keep most of the zord suits since they can be damaged beyond repair as time goes on. The Japanese company that creates the Japanese footage that is used in Power Rangers, the company's name is Toei, they do not keep the zord suits either but they typically hand their zord suits off to a Bandai Museum in Japan so they can display them for fans of the series.
Power Rangers Halloween costumes will probably be sold mainly online due to their old school vibe. Websites such as halloweencostumes4kids.com/pages/boys/PowerRangerGreen.html sell the classic suits for Halloween!
One opinion believes that the Power Rangers just simply puts them on similar to the way they put on clothes. Another opinion believes that they use the Morphing Grid in order to morph into their Ranger forms within seconds.
There is no museum that is just for Power Rangers or its Japanese counterpart known as Sentai in Japan however Japan does have the Bandai Museum. The Bandai Museum holds various things from various Sentai series such as the Mecha suits which would be known as zord suits in Power Rangers terminology. The Bandai Museum also keeps old models that the Sentai once used such as the models that were used for Power Rangers' Mastodon, Pterodactyl, Triceratops and Saber-Toothed Tiger Dinozords from the first season of Mighty Morphin Power Rangers Season 1.
They are fake, "Power Rangers" are the characters of the suits put on, the people who put on the suits are not fake, but the Power Rangers are non-existent as compared to the real people who take on their character. For that matter, when they walk through the mall going shopping, nobody screams "Wow Power Rangers!" , because its only when they put the suit on that they become a power ranger.
The power rangers series that was set in space. Think it was called Galaxies or Turbo.
The two monster suits that were combined to create Malavex for Beetleborgs are Death Mult in his first form which was an unused Beetleborgs monster and a monster that's called Parrot Top which appeared in the Power Rangers episode titled "Alien Rangers of Aquitar, Part 2."