Whipped egg white snack texture and preservation
The treat you are describing I believe is a meringue. These little guys are tricky to get right the first time, as it is all about how long you cook them for and how finely you whip the egg white mixture. What I like to do is add a bit of lemon zest on each one. Not only does it enhance the vanilla flavour (if you're using it), but it also serves to tell you when the meringue is just about ready (goes brown/near black). I have never tried adding gelatin but I don't suppose that would turn out well. 

My suggestion: Cook the meringues at about 160-180 degrees celsius, checking on them every 5-10 minutes. Press your finger into one of them if you feel they are ready (the sacrifice of one for the survival of many, I know) and keep repeating this until you feel you have reached your desired texture. The beautiful thing about them is: you can cook them a little to leave them marshmallow-ey or you can cook them into crumbly, crunchy, snacks. 

As for how long they last, meringue tend to last about two weeks without a significant change in quality in an airtight, sealed container.

Quick Tip: To keep them soft in texture, let them cool slowly in the oven with the door ajar. 

Good Luck!