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.
Also as noted above it is technically not very practical either as since she can't take it off as she can't do things like bathe herself, use the bathroom and clean it if it gets soiled though it doesn't look like the characters think that far about it.
How do so many characters in Hytopia look identical to ones who appeared in A Link Between Worlds in Hyrule? The Links in both games are the same, and unlike sequels like Link's Awakening, Majora's Mask, or Phantom Hourglass, this one takes place in the same universe. Yet we have the item seller, the stylish woman, the Kakariko shop owner...Do the characters in Hyrule all have identical twins, or did they all migrate to Hytopia for some reason?