Disappearing folder on Macbook Air
To recover your lost files, you could try TestDisk, or PhotoRec, the dedicated picture recovery version.
There's also Disk Drill, which offers a freemium product (that seems fairly easy to use). I haven't tried it.

Keep in mind that to recover files the recommended procedure is to stop using the affected disk immediately, and ideally mounting it as an external drive on another system to do the recovery from there, as space marked as free on your hard drive gets overwritten randomly.

About files appearing on "Recent" menus: it is not an indicator that the file is still on your hard drive. It is usually a link to where the file was when you opened it.