What are the little numbers in red outside of the vault?

This refers to what level of vault you can open. Currently this is 1,2 or 3.

1 currently being orange, 2 blue and 3 pink. So the number you see will depend on how many stars you currently have.

The little red number on your vault (1,2, or 3) indicates how many vault options are available to you for opening. There are 3 vault options in total. An Orange vault (250), a Blue vault (500) and a Gold vault (800). As you progress through the game and earn stickers, duplicate stickers are collected in your vault. Once you accumulate the required amount, you can choose to trade your excess stickers, or “open a vault”, for additional rewards. By hovering on the vault of your choice you can see what rewards are contained in each vault before selecting to open it.

I think you’re talking about the vault in the bottom right hand corner when you open your stickers. If so, that number signifies that you have enough stars and are able to open that number of vaults to get additional prizes