How can I make this killing script work properly?

Here's a fixed version of your script:

local part = script.Parent

local groupInformation = {}

game.Players.PlayerAdded:connect(function(player)
    groupInformation[player.UserId] = player:GetRankInGroup(2582242)
end)

game.Players.PlayerRemoving:connect(function(player)
    groupInformation[player.UserId] = nil
end)

part.Touched:connect(function(hit)
    local humanoid = hit.Parent:FindFirstChild("Humanoid")
    if humanoid then
        local player = game.Players:GetPlayerFromCharacter(hit.Parent)
        
        if groupInformation[player.UserId] == 255 then
            humanoid.Health = 100
        else
            humanoid.Health = 0
        end
    end
end)

Here's a rundown of what changed:

First off, I added this bit to the top of your script:

local groupInformation = {}

game.Players.PlayerAdded:connect(function(player)
    pcall(function()
        groupInformation[player.UserId] = player:GetRankInGroup(2582242)
    end)
end)

game.Players.PlayerRemoving:connect(function(player)
    groupInformation[player.UserId] = nil
end)

This makes it so that whenever a player joins, their rank in the specified group will be cached. It's expensive to make an HTTP request every time someone touches a brick. This way, we'll know whether they're in the group once they enter, making checking whether they're in the group mostly instantaneous.

Also note that it's always important to pcall async functions that make web requests. Something can always go wrong.

Next, I changed this:

local player = game.Players:GetPlayerFromCharacter(hit.Parent)

        if groupInformation[player.UserId] == 255 then

What you were doing before is trying to run methods on playername, which won't work, since playername is a string, not a player. What I did instead is use a method from game.Players to fetch the player object from the character model.

Next, instead of making an HTTP request to check what rank the player is in the specified group, which would be slow, we just check our cache of player ranks in that group.

I hope this helps. Good luck!