Learn Italian: Faccio calcolare il doppio della quantità. - I am having double the quantity calculated.

In Italian, doppio acts as a noun here (il doppio, meaning 'the double' or 'the double amount'). Because it is a noun, you must use the preposition di (combined with la to make della) to link it to the next noun. You are literally saying 'the double of the quantity'.

How does faccio calcolare mean 'I am having... calculated'?

This uses the causative construction, which is the verb fare followed directly by an infinitive. You use it when you get someone else to do an action for you instead of doing it yourself. While English says 'I have [something] done', Italian phrases it more like 'I make calculate'.

Why doesn't the object go between the verbs, like in the English 'I am having double calculated'?

In the Italian fare + infinitive structure, the two verbs must always stick together. You cannot separate faccio and calcolare with the object. The whole verb block comes first, followed by the object (il doppio della quantità).

Is quantità feminine, and how would I make it plural?