Airdrop

The Recently deleted folder is the only place you can find deleted photos, unless it has been more than 30 days since you deleted them. Photos deleted today should be there, unless there was a problem. If there was a problem and there is no backup of the device done since the photos were there, then there is no other way to restore them. Again, were you using iCloud photos, and do you share that iCloud photo library with anyone else?

I don't understand the problem. You say that photos were airdropped to you, then you couldn't see them, but then you could. I'm not sure I know your question. Do you want to know why you couldn't see them then could? Where are you looking for the photos at? If someone airdrops a photo, it should immediately appear in your Camera Roll.

If you deleted photos from your Camera Roll, they would be in the Recently Deleted folder. Are you using iCloud photos?

Once they have been airdropped and saved on your device, they cannot be deleted by someone else.

Not once you have accepted the photos. They are downloaded to your device.