Help in using D600! Manual focus point?

I'm just a new Nikon D600 user and not familiar with my first FX body. I would like to know if I can similarly do the focus selection on the D600 like that of the old Nikon D80.
The old Nikon D80 has the manual focus point selection wherein if you half-pressed the shutter button, the camera will make the image clear even if in Manual Focus Point Selection

Does the Nikon D600 has this kind of Manual Focus Point Selection wherein the camera can automatically detect the subject that make it clear
If there's such a setting how do I do it?

I have tried switching the M/A button on the lens and on the camera.

All it gives me is autofocus, AF-S, AF-C etc.
I tried different lenses Nikon G, D lens even 3rd party lens but nothing
When in Manual Point Focus Selection, I can select focus manually, obviously; but the camera does not have the ability to focus automatically when the shutter button is half pressed
On the Nikon D600, all I get is autofocus and it is not that reliable, unlike in using the old Nikon D80 manual focus point selection mode I can focus it wherever I want and it detects the subject making it clearer.

I don't have a D600 but this info will be in your user manual. I do have a D300 and I would suggest that you switch to a single point AF (rather than multiple point AF).By default you have multiple points selected. This way you can be sure what the camera is focusing on (I usually use the central single point). You half shutter press to focus & then re-compose if necessary.

In autofocuus?

You should have a Live View option?

I have a D5100 and there's a lever attached to the selection dial for Auto, Scene etc - when I flick this I get the actual image in my display. As soon as push down on the round button on the back that you use to flick through and look at pictures you have taken it shows a box for focus so you can move it around to tell it where to focus.

In manual focus?

When you look through the view finder you will see multiple focus points. When you push halfway down the default is the centre focus spot. Use the round wheel thing at the back to move the focus point around (this works without having to push down the shutter button). Go sideways if you want to move it to the left or right… You get the picture (pun intended).

I'm confused. You talk about manually choosing the AF spot and then you talk about the camera choosing it for you. I will walk you through some of the procedure and you can use what you need.

The key is in pressing the little button in the center of the AF-M switch on the body by the lens. While holding the button, turn the command dial (thumb) and it cycles thru AF-A, AF-S, and AF-C. Select AF-A. Now, turning the sub-command dial (front) will let you choose S, C, and various other options like Auto, 3D, 9d, 21d (I think). Try either Auto or 3D and see if this is what you are looking for.

If you set the camera or lens in manual focus, I don't understand how it would "focus automatically when the shutter button is half pressed."