I checked yesterday and one of the AF-S or AF-C settings was on release. After ensuring they were both on Focus I took several shots and just downloaded them and all of them had focus points displayed when uploaded and viewed on my computer. So maybe that is my issue there. But my focus issues are still there.When I take pictures using the 55-300 MM VR lens I can getclose up portraits to be focused butwhen I take pictures of birds with the focus right on thesubject it is blurry. It also happens with my 35 MM Prime lens. Even when I getone that appears to be focused and I try to crop it, it is blurry.
I uploaded four pictures and hope I did it right. The one of the flowers is the only one that is in focus where the focus point shows.
You mention "focus point
s" (plural). Now this could be part of your problem. You have to understand that when you let the camera decide which focus point it should use, it doesn't know what you are trying to photograph. It only looks for the best contrasty thing to focus on. In the case of your birds shots, there are a lot of branches in the background and I suppose the camera focused on them instead of the bird.
I would suggest you switch to AF-S single point focus and set the bird right on your focus target. This way you can then evaluate if the focus is OK or not. Whenever you work with multiple focus points, you could get cheated by the camera's focus selection.
In the owner's manual, there is a page where Nikon explains certain situations where autofocus doesn't do great, and your bird and branches falls right into these situations.
I have a D7000 and only use one focus point and find I get better focus results with this. Good luck.