Why it won't select randomly sound values from the list?

Basically it loops so fast through all the sounds, and you don't hear any of them until the loop ends and it plays the last song.

Just wait inside the loop for the sound to end. You can only do this in a Local Script.

--// Local Script:

local sound = script.Parent.Parent.PlayableSound
local musicList = script.Parent.MusicList

for _, music in pairs(musicList:GetChildren()) do
    sound.SoundId = "rbxassetid://".. music.Value
    sound:Play()
    sound.Ended:Wait() -- Wait for the sound to end.
end

Edit:

As for making it random, you need to use math.random().

You can index a table using a number to get a direct value within the table. Using math.random, and getting the size of the table using #table, we can get a random music.

--// Local Script:

local sound = script.Parent.Parent.PlayableSound
local musicList = script.Parent.MusicList:GetChildren()

while true do
    local music = musicList[math.random(#musicList)] -- Random Music
    sound.SoundId = "rbxassetid://".. music.Value
    sound:Play()
    sound.Ended:Wait() -- Wait for the sound to end.
end