This is getting interesting. I just switched to Nikon and have a D3200. I shoot Raw+Jpeg and both look the same when I open in Nikon's View NX2. In the two different above pictures, you mean they were taken during the same shutter snap? I can understand if you changed to Jpeg only there might be a difference. Another possibility is that on my Nikon there is a "Portrait" setting among several options in one of the menus: 'shooting menu' under 'picture control'; Portrait mode gives muted color, but good detail in the shadows for post processing; "Landscape" mode gives much more contrast and color. There is also a Neutral and Standard, Vivid and Monochrome in addition to Portrait and Landscape. And even as I type this I have discovered something else as I examine my camera: when I choose Portrait or Landscape, etc. mode and 'right click' on the circular pad with an 'OK' button in the middle, a new window pops up with adjustments for saturation, contrast, sharpening, hue and brightness, that I didn't know about. If your camera has this,( and I haven't heard it mentioned yet), it may offer more options to find the right tones for your washed out photos.

The strobe effect tells two things, 1 that your flash is working and 2 that you are indeed in Camera iTTL mode and not commander mode (as you have repeatedly said).

I have just two cards left to play.

Being new to this camera and its complex menu system, are you aware that there are four banks of custom menus, A, B, C and D, and that even if you set items in one bank they will not work unless you are shooting from that bank?
You probably are aware of this but it can happen.

My last bullet is the EV setting for the flash. Press and hold the little button just below the flash pop-up button, the control panel should show 0.0, if it doesn't use the sub-command dial to zero this number.

Reshoot and post a picture, tick the "download original" box and we can look at the extended Exif data to try to work out what is going on.

Using on board pop-up flash will put hard unsightly shadows all over the place behind your subjects but the are no such shadows present in your images. There is no sign of a catchlight in the dog's eye, nor any sign of a flash reflection on the green box. In the Pepsi Cola bottle their are three catchlights, I think one may be a computer screen or TV, the second is possibly a window, the third may be your flash but very underpowered, as would be expected in commander mode. All three pics are between 1.3 and 2 full stops under exposed with the only lighting detected by the camera being ambient window light.
The message you are getting about no return light being detected appears to be correct for the conditions in so far as the flash light is not illuminating the subjects.
I assume your camera batteries are in good order and you are leaving enough time between shots for the flash capacitor to recharge, I also assume the pop-up is popped up!
Test the flash:
Open the menu, go to the Pencil Icon and choose e Bracketing/flash. Then choose e4 Modeling flash and turn this on.
Aim your camera and press the Preview button on the front of the camera.
Did you get "Nothing at all" or a couple of "diminutive flashes" or a "whole burst of flashes which lit up the room"?
Try this first, tell me the results and then we can move on