Learn Russian: У вас есть с собой ключ от шкафчика?

The reflexive pronoun себя (which becomes собой in the Instrumental case) always refers back to the logical subject of the sentence. Even though ключ (the key) is the grammatical subject in an У вас есть construction, you are the person logically possessing the key. Whenever you say 'I have with me' or 'you have with you', Russian uses с собой.

Why does the sentence use от шкафчика to mean 'locker key'?

In English, we usually say the key 'to' a lock or door, but in Russian, you use the key 'from' it. You must use the preposition от (from) followed by the Genitive case. So, 'the key to the locker' translates as ключ от шкафчика.

What is the base word for шкафчика?

The base word is шкафчик (a locker or small cabinet). It is a diminutive form of the word шкаф (cupboard or wardrobe). Because it follows the preposition от, it takes the Genitive case ending and becomes шкафчика.

Does it matter where I put с собой in the sentence?

Russian word order is very flexible. You could also ask У вас есть ключ от шкафчика с собой? Putting с собой right after есть just slightly emphasizes the 'on your person right now' part of the question.