Learn Arabic (Modern Standard): يا أختي، أضيفي الزيت الآن.

Because the speaker is telling a female (أختي, meaning 'my sister') to do something. In Arabic, when you give a command to a single female, you must add the suffix ـي to the end of the verb. If you were talking to a male, you would use the masculine form without the suffix: أضف.

Is the ي at the end of أختي the same as the one on the verb?

They look exactly the same, but they do different jobs! On a verb like أضيفي, the ـي shows that you are giving a command to a female. On a noun like أخت (sister), the ـي is the attached pronoun meaning 'my'. So أختي means 'my sister'.

Why do we need the word يا at the beginning of the sentence?

The word يا is a 'calling word' (vocative particle). In Arabic, whenever you address someone directly to get their attention, you must use يا right before their name or title. While in English we just say 'My sister, add the oil', Arabic requires saying 'O my sister'.

Why does the command أضيفي start with an أ (alif with a hamza) instead of a plain alif?

The verb for 'to add' belongs to a specific family of verbs that always keep a strong 'a' sound (the hamza) at the beginning of their command forms. For many other basic verbs you've learned, the starting alif is just a 'bridge' that goes silent in the middle of a sentence, but this أ is always pronounced.