can this script be used to unanchor parts on player's touch?

I'm thinking your problem is..."player" is the player stored in game.Players and touched is the part that touched the detector (the players foot). You need detect if the part that is touching the detector is the players character. You then need to get the player instance from the players character(if you use that to compare).

You can do this like so...

game.Players.PlayerAdded:Connect(function(player)
    script.Parent.Touched:Connect(function(hit)
        local playerhit = game.Players:GetPlayerFromCharacter(hit.Parent)
        if playerhit then
            print("Hi there")
        end
    end)
end)

Sorry, not the greatest at explaining things so here's some documentation: https://developer.roblox.com/en-us/api-reference/function/Players/GetPlayerFromCharacter

Edit: You also need to change your variable set up. Doing it like this

local hp = script.Parent.Part1 and script.Parent.Part2 and script.Parent.Part3

will only change properties for part3

I recommend setting it up like this

local hp,bh,tp = script.Parent.Part1,script.Parent.Part2,script.Parent.Part3

or iterate through a model

local model = script.Parent

for i,v in pairs(model)do
    if  v:IsA("Part")then
        v.Anchored = false
    end
end

Please do upvote if this helped ;)

ok look the script in in > HatchPiece3 if its in hatchPiece3, its cant get hatchpiece 2 by script.Parent you would probably do this >

game.Players.PlayerAdded:Connect(function(player)
local hp = script.Parent.HatchPiece1 and script.Parent.Parent.HatchPiece2 and script.Parent.Parent.HatchPiece3

hp.Touched:Connect(function(touched)
if player == touched then
hp.Anchored = false
end
end)

end)

and put all these parts to the model