Why can't I adjust the Value of a BoolValue?

This is actually a really simple fix!

You see, where you put the value is not ideal, because each time they spawn they get the same false value from starterpack. Because you set the value to true in each player, then spawn them, it's giving them a False valued BoolVal once they spawn. So when you set the value in each player to "true", but then spawn them in, then it "refreshes" their backpack, giving them the false valued BoolVal.

What I suggest is putting the value in the player as soon as they join using Instance.new. This is better because you can easily edit each player's value without having to go into backpack.

Here's what i'd do:

game.Players.PlayerAdded:connect(function(plr)
a =I nstance.new("BoolValue")
a.Name = ("InGame")
a.Parent=p
a.Value=false
end)

For the first script, i'd simply change it to:

local plrs = game.Players:GetChildren()
for _, child in ipairs(plrs) do
    child:WaitForChild("InGame").Value = true
    child:LoadCharacter()
end

For your second script, i'd edit a few lines like this:

for k,player in pairs (game.Players:GetPlayers()) do
    player.CharacterAdded:connect(function(character)
        if player:WaitForChild("InGame").Value then
            character.Humanoid.WalkSpeed = 30
            character.Humanoid.JumpPower = 200
           end
        end
    end)
end