Workspace and Server Replication?

Hey there!

Lets look at both of your problems.

GuiButton that creates part visible to Server and Client

This one is easier than you might think. All you have to do, is create the part server-side, and it will automatically replicate to the clients.

To accomplish this, set up a RemoteEvent that fires to the server once you click the GuiButton.

Client

local repstore = game:GetService("ReplicatedStorage")
local CreatePart = repstore:WaitForChild("CreatePart") --RemoteEvent
local gui = script.Parent

gui.MouseButton1Click:Connect(function()
	CreatePart:FireServer()
end)

Server

local repstore = game:GetService("ReplicatedStorage")
local CreatePart = repstore:WaitForChild("CreatePart") --RemoteEvent

CreatePart.OnServerEvent:Connect(function(player)
	local char = player.Character
	if char then
		local p = Instance.new("Part")
		p.Size = Vector3.new(1, 1, 1)
		p.Color = Color3.new(1, 0, 0)
		p.Shape = Enum.PartType.Ball
		p.Anchored = true
		p.CanCollide = false
		p.CFrame = char.HumanoidRootPart.CFrame * CFrame.new(0, 0, -5)
		p.Parent = workspace
	end
end)

Sending the Mouse through a Remote to the Server

This is not possible. You cannot send the actual mouse object through a remote, because it is strictly client-side.

However, you can send the position where the mouse clicked, and/or the BasePart the mouse clicked on.

Client

local repstore = game:GetService("ReplicatedStorage")
local SendMouseInfo = repstore:WaitForChild("SendMouseInfo") --RemoteEvent

local players = game:GetService("Players")
local player = players.LocalPlayer
local mouse = player:GetMouse()

mouse.Button1Down:Connect(function()
	local target = mouse.Target
	local hit = mouse.Hit
	if target then
		SendMouseInfo:FireServer(target, hit.p)
	end
end)

Server

local repstore = game:GetService("ReplicatedStorage")
local SendMouseInfo = repstore:WaitForChild("SendMouseInfo") --RemoteEvent

SendMouseInfo.OnServerEvent:Connect(function(player, target, position)
	print("player: "..player.Name)
	print("target: "..tostring(target))
	print("position: "..tostring(position))
end)