Marcus Munitions is the shop in Borderlands Mobile. You can purchase loot chests from Marcus Munitions:

• Free Chest - Contains a Common Weapon. You can claim a Free Chest every 10 minutes. The timer will only reset once you have collected your Free Chest.
  

• Golden Chest - Can be purchased with 1 Rare Key and it contains a Rare Gear.
• Epic Chest - Can be purchased with 3 Epic Keys and it contains an Epic Gear.
• Legendary Chest - Can be purchased with 5 Legendary Key Fragments and it contains a Legendary Gear.

Note: The Costumes tab will be available soon.