Let's sat I want to quit my vault and start over will I get all of my in-app purchases back to use on the next vault?

No, gone forever if you delete the vault. All purchases and earned lunch boxes are vault specific.

I recommend pick a few dwellers, send them out into the wasteland. Delete all but 10 of your best items (no storage room needed) and then deleting all rooms. Then call the dwellers back.

Just like starting over, except without losing what you got from lunchboxes, plus whatever caps you've accumulated.

Did you actually try?

How is the objectives like that?

Objectives are based on dweller count, I think. Maybe average dweller level too. So objectives depend on what sort of dwellers you keep, and how many. You can make sure to only keep low level ones, but I didn't play around with it much, so not absolutely sure.

..but if you mean the newbie starter objectives (like rush two rooms = lunchbox) no, you don't get those again.

Oh man, those were great!

I spent about 5 days creating a vault and going through the first few cupcake objectives that offered lunchboxes in an attempt to get the Heavy Wasteland gear (for the massive hit point boost while equipping it to a level 1 dweller with 10 endurance and riding it all the way to level 50). If I didn't get what I wanted after a handful of lunchboxes, I deleted the vault and started over.

I got pretty dejected after a few days of trying and not getting what I was looking for... then all of a sudden I got not one, but TWO Heavy Wasteland outfits AND the freaking MIRV! Greatest day in the history of Fallout Shelter.

^^ This also leads me to believe that the game is programmed to offer up a high ratio of legendary items from lunchboxes early on. I'm sure it's a way to try and lure new players in.

"Oh man, look at all these cool ultra-rare items I'm getting super early in the game. This is easy, I'm going to start playing this regularly to get even more great stuff! Yay!"

I don't know where the trigger is, but I'm assuming after your vault grows to X amount of dwellers, the ratio plummets. Or maybe it even goes by lunchbox count, after opening X amount of lunchboxes you start to get saturated with crappy loot. I would be most interested to find out what the story is there.