You should be able to recover them. If you go into your files you should be able to see the contents of your "trash" which will contain your deleted items.
On my phone (android) you go to Tools\storage\trash
Without a biopsy it's impossible to tell if a tumor is malignant or not. I would let the bird live its life as long as its eating, drinking, and pooping normally. If the quality of life begins to drop you may consider culling, but until then, I would just observe and let it be.
It might be a cyst from getting pecked, it might be a tumor. It looks clean, so I'm guessing that you've been making sure that it stays clean, which is a good first step. I'm not sure what else you can do unless a vet is an option.
I have to agree with @Susan Skylark. If that is prolapse that has been out long enough to dry up like that, it could be serious, but again, the first thing to do is that epsom salt bath. Make sure to keep them warm so they don't get chilled after their soak.
Check out the articles in the learning center on quail. There is one on incubation that tells a bit about the different types of incubator.
https://www.backyardchickens.com/articles/category/quail.32/
It doesn't sound like the prolapse is environmental, then. I would start with the epsom salt baths and if you can, keep their home dim for a week or two to let them relax and heal.
Start with a warm epsom salt bath. This should be about quail body temp or a few degrees warmer.
It's rare for males to have prolapse.
Are you handling them a lot?
What are you feeding them?
Are they eating and drinking normally?
What is their home setup like?
Does their poop look normal...
Check with your local ag department to make sure that you either don't need permits or have the ones you need. They may also have some good advice for you.