The Sword Suit and the Sword Master Suit look the way they do because they are straight upgrades to the Hero Suit Link gets at the start of the game.
Adding to this, the Sword Suit looks like it might be based off of the attire of the Hytopian guard, seeing as it's blue with red and gold accents. The Sword Master Suit, meanwhile, seems to take inspiration from the soldiers encountered in the Sky Realm with its golden armor and cape.
During the final battle against The Lady her second and third phase has her putting her version of the Sword Suit and Sword Master Suit that Link gets.
Why is the Hookshot replaced with the Gripshot when the two items have no differences in ability or usage? Because using the Hookshot on another Link would impale them.
When trying to get it off the king summoned his strongest men to take it off so she probably was victim to being touched in many places, by many men, considering that it's so tight.