Yes, but you are limited in what you can change because jpg's do not contain all the information that was in the original RAW data. Remember, neither RAW, jpg, gif, or any other format files are actual photographs. They consist of millions of "1's" and "0's" that when processed by appropriate software result in a visible photograph. If you want the maximum ability to control what your final photograph looks like, you should always work from a RAW file.

As to the fact that every camera manufacture use there own RAW formats, that is not a problem since they all provide software for viewing their camera's RAW files (for cameras that will output RAW files for the user) and Lightroom and Photoshop, the industry standards for editing, recognize all the different RAW formats.

Using an FX lens in the DX mode makes no sense at all because you will gain nothing. In DX mode, your camera is using only a portion of the sensor that restricts the resolution to about 16Mp. That is equal to the resolution you will have by cropping a picture taken in the FX mode to match the DX mode picture area. I.e., you will end up using the same number of pixels and, therefore have the same resolution either way. I have the f2.8 24-70mm lens and because of the 36Mp starting resolution am able to get sharp high quality photographs by cropping to a point that I am using less than the DX portion of the sensor. If you are making big enlargements and need high resolution, you should invest in an appropriate focal length FX lens and forget about playing games.

You may have lost your pictures, but there is an important lesson to be learned for everyone from you desaster. ALWAYS verify your file transfer before formating the original media and ALWAYS BACKUP YOUR FILES! There are many ways to do that. Cloud backup is good if you have a relatively few number of pictures. Because I always shoot in raw and each exposure is at least 40Mb that is cost prohibitive for me. Instead, I use a Drobo, which is a RAID (Redundant Array of Independent Disks) system. My main files are downloaded to a 5TB external hard drive that is used only for photos. Copies of those files are automatically written to four 5TB hard drives in my Drobo. If any of the hard drives become corrupted, I still have multiple backups of my data. That does not, however, protect my files in case of a catastrophe such has a house fire. Offsite backup is also required for complete protection.

For offsite backup without the expense of cloud backup, I periodically copy my main photo hard drive to another hard drive and store it at my son's house. This strategy actually requires two drives. Every two weeks, I copy my data to one of those two drives and take it to my son's house. I take the other drive from my son's house home and use that for the next bi monthly backup. If you don't have a child who lives near by, you can keep your drive in you car's locked trunk, in a bank safe deposit box or elsewhere.

When I was 13 years old, I received a Kodak Pony 135 as a gift. When I grew out of it as a freshman in highschool, I moved up to a Miranda DR. At that age, I fell for their Popular Photography ads with the girl in the bikini. Besides that, at $169.95, it was one of the least expensive SLR's on the market. Later, I attended Brook's Institute of Photography in 1964 and bought a Nikon F Photomic. Since then I have stuck with Nikon. I currently have D800's.

Rather than spending the money on a "kit" lens, do this. Buy the camera body only. For $150 or less on E-bay, you can buy a 70-300mm f/4-5.6G AF Zoom-Nikkor lens. This is an FX lens that will work on any modern Nikon digital SLR including the D7100. It has a big advantage for wildlife photography because it is an FX lens. When used on a DX camera, it has the effect of using a longer focal length lens. In fact, at the 300mm setting, it is the equivalent of a 450mm lens. For everything else, Adorama in NYC has a used 28-70mm f/2.8 ED-IF AF-S Wide Angle-Telephoto Zoom-Nikkor Lens for $250.00. They are a very reputable company. You can find the lens at this ULR: https://www.adorama.com/us%20%20%20%20815239.html?gclid=Cj0KEQiAh4fEBRCZhriIjLfArrQBEiQArzzDASIjPhlLZngD3cEiIWoC-JCp3QJVc7Y_K7E2lk5cCxsaAkmX8P8HAQ

I have been buying most of my equipment from Adorama for years. They are located near B&H in Manhattan, NY and are a direct competitor. There prices are about the same. In fact, both Adorama and B&H are asking $526.95 for the 35mm f/1.8G AF-S ED Nikkor lens. Adorama includes some accessories that B&H does not. Both companies are outstanding on customer service and returns and both do not charge sales tax if you are in a state like California.