Can i make a local script that detects what a other player says?

Sure, just connect Chatted to other players, except in a localscript. You will have to account for already existing players tho, instead of just connecting to PlayerAdded.

local function Chatted(plr, msg)
    print(plr,"said",msg)
end

local function PlrAdded(plr)
    plr.Chatted:Connect(function(msg)
        Chatted(plr msg)
    end)
end
game.Players.PlayerAdded:Connect(PlrAdded)

for i,v in pairs(game.Players:GetPlayers()) do
    PlrAdded(v)
end