To know if you're using the Intel HD 3000 (Main Graphics card), append in Termina the following:

/usr/lib/nux/unity_support_test -p

You should get a similar result as the following:

OpenGL vendor string:   Tungsten Graphics, Inc

OpenGL renderer string: Mesa DRI Intel(R) Sandybridge Mobile 

OpenGL version string:  3.0 Mesa 8.0.2



Not software rendered:    yes

Not blacklisted:          yes

GLX fbconfig:             yes

GLX texture from pixmap:  yes

GL npot or rect textures: yes

GL vertex program:        yes

GL fragment program:      yes

GL vertex buffer object:  yes

GL framebuffer object:    yes

GL version is 1.4+:       yes



Unity 3D supported:       yes

Try again with the nvidia card (that, if Bumblebee is successfully installed):

optirun /usr/lib/nux/unity_support_test -p

You should get:

OpenGL vendor string:   NVIDIA Corporation

OpenGL renderer string: GeForce GT 525M/PCIe/SSE2

OpenGL version string:  4.2.0 NVIDIA 295.40



Not software rendered:    yes

Not blacklisted:          yes

GLX fbconfig:             yes

GLX texture from pixmap:  no

GL npot or rect textures: yes

GL vertex program:        yes

GL fragment program:      yes

GL vertex buffer object:  yes

GL framebuffer object:    yes

GL version is 1.4+:       yes



Unity 3D supported:       no

Know that The Nvidia card is not compatible with Unity 3D. The Intel HD 3000 is. That means that if you're using Unity 3D now, it's the Intel card which is in use.
And the fact The Graphics Driver name does not appear in Systems Settings (Details), stipulates there is some conflict between drivers (Proprietary drivers of Nvidia or Nouveau).
Purging them and reinstalling bumblebee seems a solution (Bumblebee will resintall Nvidia drivers nvidia-current for you).
The correct result should look this:

OR:

You quoted : "And if I go to System Settings > Additional Drivers, it returned nothing in the list and only with a description "No proprietary drivers are in use on this system"." -> This is normal when you install Bumblebee and normal when the Nvidia card is not activated and not recognized by the system. I am having the same thing and it's not an issue.
You can trace eventually what happens in the video log: /var/log/Xorg.0.log

For your other tweaking needs.
As you're new to Ubuntu, the best way to achieve some tweakings for your whole desktop is to install the application: UBUNTU TWEAK, this way:

sudo add-apt-repository ppa:tualatrix/ppa

then

sudo apt-get update && sudo apt-get install ubuntu-tweak