In a world that has both the capacity to read other people's minds, and a truth potion so powerful that a few drops has them spilling their inner most secrets. Why do they have normal trials relying on witnesses and questioning?
Ethics. You shouldn't force people to undergo a magical procedure.
In Gringots there is "The thieves downfall" which is a waterfall that removes all enchantments, including the imperious curse. Why does the ministry of magic not have a feature of this kind? That would eliminate the worry of people in power being controlled.
If "The Thieves Downfall" removes all enchantments, why do you think it can be enchanted to work elsewhere?
Gringotts aren't going to allow any old so-and-so to be magically moving through a part of their catacombs.
You can use an simple charm to make yourself completely invisible, and most spells require you to hit the target, why was this spell not used at all to help in a duel? Being invisible would help ALOT without protection. On the same note, spells can be cast under the invisibility cloak, why did harry never take advantage of this?
It's extremely hard to make yourself completely invisible using a disillusionment charm. The time would be better spent on other defensive or offensive spells.
Harry is an idiot, welcome to the series.
Harry potter protects a cloak that is makes him 100% invisible. Why do they just drop it on the ground and completely forget about it and just leave it lying around?
See above.
The cloak is supposed to protect you from death itself, but mad eye's fake eye can just see through it like it was nothing?
It's widely agreed that the story of The Three Brothers is
just a fairytale, and that the Deathly Hallows were really just made by a very powerful family of old wizards.
Glad we cleared that up.