How To Copy A Whole Model?

You can simpy clone the Tree model. The clone will contain cloned descendants aswell.

As for setting the transparency, use a for loop.

And to position it, use SetPrimaryPartCFrame() function of the model, but first, set the PrimaryPart property to the main part of the model in your properties window in studio.

Also, your script wouldn't work outside of studio due to how you use LocalPlayer and ServerStorage.

Here's a fixed FE compatible script:

Server script:

local event = Instance.new("RemoteEvent", game:GetService("ReplicatedStorage"))
event.Name = "plantTree"

local function SetTransparency(p, t)
    for i,v in pairs(p:GetChildren()) do
        if v:IsA"BasePart" then
            v.Transparency = t
        end
    end
end

event.OnServerEvent:Connect(function(plr, pos)
    local Tree = game.ServerStorage.Tree:Clone()
    Tree:SetPrimaryPartCFrame(pos)
    Tree.Parent = workspace 
    wait(10)
    SetTransparency(Tree.Tree1, 1)
    SetTransparency(Tree.Tree1.Tree2, 0)
    wait(0.1)
    Tree.Tree1.Tree2.Leaf1.Transparency = 0.4
    Tree.Tree2.Leaf2.Transparency = 0.4
    wait(10)
    SetTransparency(Tree.Tree1.Tree2, 1)
    SetTransparency(Tree.Tree1.Tree2.Tree3, 0)
    wait(0.1)
    local tree3 = Tree:FindFirstChild("Tree3", true)
    for i,v in pairs(tree3:GetChildren()) do
        if v.Name:sub(1, 5) == "Leave" or v.Name == "Particle" then
            v.Transparency = 0.4
        end
    end
    tree3.Particle.ParticleEmitter.Enabled = true
end)

Local script:

local event = game:GetService("ReplicatedStorage"):WaitForChild("plantTree")
local mouse = game.Players.LocalPlayer:GetMouse()

mouse.Button1Down:connect(function()
    event:FireServer(CFrame.new(mouse.Hit.p))
end)

I believe I found your problem. GetChildren() is a function, meaning you need to place brackets after you write it. So instead of

Tree.Tree1.Tree2.GetChildren.Transparency = 0

you need to have

Tree.Tree1.Tree2.GetChildren().Transparency = 0

However, GetChildren() returns a table of objects, so it has no Transparency property. To change the Transparency of every item in the list, you need a for loop:

local aList = Tree.Tree1.Tree2.GetChildren()
for child in aList do
    child.Transparency = 0
end

I hope this answers your question, if no, tell me and I'll fix it my answer.