How to make the player's camera, is fixed, and you can't rotate it, but the mouse can still move?

There are multiple ways to do this.

One way: You can set the CFrame-position of the camera.

local camera = workspace.CurrentCamera
camera.CameraType = Enum.CameraType.Scriptable
camera.CFrame = CFrame.new(CameraPosition, CameraLookPosition) -- the camera will be at the first position and look at the second

Another way: You can change the CameraType of the camera.

local camera = workspace.CurrentCamera
camera.CameraType = "Fixed"

There are also multiple articles on this topic on the Roblox Developer Hub.

Just set the Camera's CFrame to a fixed position. It would be something like this:

local Camera = workspace.Camera
Camera.CFrame = CFrame.new(--[[Where you want the Camera, Direction it's looking in.]]--)