The in camera is just a quick format and in some cases might not map around bad sectors. The computer format won't either, unless it's the full or long format, which will take quite a while. Quick Format just deletes the directory and sort of resets the File Allocation Table. It does not read or write every location. The in-camera format also sets up the directories that the camera expects to see.
I have had good success doing an occasional full format and maybe even running diagnostics in my computer, but always reformat in the camera before use. All of the benefits of the computer format are preserved, and files are set up properly.

I would find another shop to buy your gear from and get advice.

There is no 4X extender, and they are TELE extenders, intended to work on relatively fast telephoto lenses, and a few select short range zooms, like the 70-200 and the 200-400. Some third party lens mfgrs make a 1.4 for their 150-600, but results are not amazing. The Tamron G2 and the Sigma Sport are quite sharp, but when your max aperture is only F6.3, adding a 1.4X TC will make that F9 or so - and many cameras have a problem autofocusing, and if they do manage to autofocus at all, the lens will hunt in all but the brightest, most contrasty light.

There are only a few ciircumstances where a teleconverter added to a lens provides excellent results - with the Nikkor 200mm F2, Nikkor 400mm F2.8, 300mm F2.8 and the new Nikkor 70-200 F2.8 FL - these are amazingly sharp and fast lenses and they work well with 1.4x and in some cases 1.7x and 2.0x teleconverters.

You are almost always better off with a lens that is not used with a TC.

The problem with Geek Squad, and other services like them, is that they usually don't try to save files prior to wiping your computer. Up to that point, your photos, documents, etc were recoverable. If you have any friends that are a little computer tech savvy, you or them, can download a bootable copy of Linux Mint to a USB drive, boot your computer from the stick (Windows systems, I don't know a thing about Apple) and copy your files off to another stick or a removable hard drive. The malware won't affect the Linux boot and your files will be fine unless they were infected by the malware or corrupted install, which generally is not the case.

This is just offered in the spirit of helping Hoggers somewhere down the road. If you have important "stuff" on your compromised system, don't just automatically let someone wipe the drive. Unless a drive is totally failed, you usually can recover your files.

Your first image is ok, but I am pretty sure any softness you are seeing is from diffraction - you used F20 on this one.

With the eagle shot I am perplexed about your camera settings - ISO 6400, I/8000 sec, F6.3 . A better combination would have been ISO 800, 1/1000 sec, and F6.3. Any chance of recording fine detail is lost in the noise. Lower ISO, using Mode 1 on VC, would have given you a better quality image. If this was not shot as a raw file,

I disagree with the notion that you have a focus issue. If is due to a focusing error then something should be in focus. There are many leaves at the eagle's distance and slightly in front of and behind the eagle. A focus calibration issue would look like either front or back focusing.

Given the size of the eagle, I am going to take a guess and say you must have been at least 300 yds away.

The image below was taken at a distance of about 250 yds, using a 600mmF4 and a 1.4 extender on a D800, 14 bit lossless compress raw file. Even though it is fairly crisp there is no real fine detail. The second image is the shot it was cropped from.