Let me answer this bullet point by bullet point.
When this item is held by a Pokémon, the holder's Speed is reduced by 50%. If the holder is of the Flying-type or it has the ability; Levitate, it becomes susceptable to Ground-type moves. Source
The holder's speed is reduced by 50%. Say a Pokemon has a speed stat of 148, with an Iron Ball it has a Speed Stat of 74. If it then becomes slower than its opponent, it will move first.
Raising/Lowering Speed Stat
If you use a move like Agility to raise your speed in Trick Room, you still raise your speed. Say that same Pokemon with a speed stat of 148 uses Agility. It now has a speed stat of 296. If it becomes faster than its opponent, it will move last. Vice versa is true as well.
Trick Room reverses the move order within each priority bracket so that Pokémon with a lower Speed stat attack first, whilst those with higher Speed stat will attack last. Individual brackets are still maintained; moves in higher priority brackets still work before moves in lower ones regardless of Trick Room. This effect lasts for five turns. Similar to Magic Room and Wonder Room, using Trick Room while it is already in effect will end it immediately. Source
Effects that alter the order of specific priority brackets override Trick Room. Therefore, Pokémon holding Full Incense or Lagging Tail and Pokémon with Stall will go last in their priority bracket regardless of their Speed stat. Pokémon activating Quick Claw will go first in their priority bracket. Source