Workspace.gamehandler:21 attempt to index nil with 'HumanoidRootPart'?

wait(11)

while true do
h = Instance.new ("Message")
p = game.Players:GetChildren()
randplayer = p[math.random(#p)]
randplayer.TeamColor = BrickColor.new("Really red")
randplayer.Character:BreakJoints() 
m = Instance.new("Hint")
m.Parent = workspace
m.Text = randplayer.Name.." was chosen as the Human! "
wait(3)
m.Parent = nil
h.Parent = workspace
h.Text = "Plushies! You have 10 minutes to survive!"
    wait (5)
    for _, plr in pairs(game.Players:GetChildren()) do
        plr.Character.HumanoidRootPart.CFrame = game.Workspace.bluespawn.CFrame
    end
    h.Parent = nil
randplayer.Character.HumanoidRootPart.CFrame = game.Workspace.redspawn.CFrame
hm = randplayer.Character.Humanoid

    hm.MaxHealth=300
    hm.Health=300 
wait(600)
for i = 1,#p do
if p[i].TeamColor == BrickColor.new("Really red") then
p[i].TeamColor = BrickColor.new("Pearl")
end
end
h.Parent = workspace
h.Text = "End of game"
wait(4)
h.Text = "Get ready for the next game"
wait (4)
h.Parent = nil

end 

Right now you realise that p is game.Players:GetChildren()... and game.Players:GetChildren().Character isn't a thing and will definitely cause an error which is the error you stated

This is extremely difficult to read because of the variable names and the terrible indentation but I think I found the issue. You set "p" as a table of all the players at the start of the loop, but you try to use it like a player on line 21. Instead, loop through every player in the table using a for loop.

One thing to keep in mind is that you shouldn't cache a table of players in a variable, because someone can leave at any time and it would cause an error if you try to access a player that doesn't exist. You should call Players:GetPlayersor Players:GetChildren every time you want to do something with every player

for i, player in pairs(game.Players:GetPlayers()) do
    if player.Character then -- make sure the player has a character so that it won't error if they are respawning or something
        p.Character.HumanoidRootPart.CFrame = game.Workspace.redspawn.CFrame
    end
end