Learn Arabic (Modern Standard): متى تأكلون دجاجا أو سمكا؟

In this sentence, 'or' is أو. Unlike the word for 'and' (و), which attaches directly to the front of the next word like a prefix, أو stands alone as its own separate word with a space after it.

Why do the words for chicken (دجاجا) and fish (سمكا) have an extra Alif and two little dashes at the end?

That ending is called 'tanween fath'. It shows that these words are the direct objects of the verb (they are the things being eaten). In Arabic, when a word is the object of a sentence and doesn't have 'the' (ال) in front of it, we usually add an extra Alif and this double-dash ending to make an '-an' sound.

Why does the verb تأكلون have ـون at the end instead of just being تأكل?

The ـون suffix shows that you are talking to a group of people ('you all'). The prefix تـ at the beginning tells us the doer is 'you', and the ـون at the end makes it plural. If you were asking just one man, you would simply use تأكل.

The first word متى ends with a letter that looks like a Yaa (ي) but doesn't have dots. How is it pronounced?

That letter is called Alif Maqsura (ى). Even though it looks like a Yaa without dots, it is actually pronounced as a long 'a' sound. So, the question word for 'when' is pronounced 'mataa'.