Ordering food

Korean names the thing first and counts it second, so the order is 'bibimbap one, please', not 'one bibimbap, please'. English does the same on an invoice or a shopping list ('apples, 3'), and that is the right picture to keep in mind: item, then quantity. 주세요 comes from 주다, 'to give', in a polite request form, so the whole sentence is literally 'bibimbap one, give'. There is no word for 'me' because it is obvious who wants the food.

좀 is a shortening of 조금, 'a little'. Put into a request, it makes the thing you want sound smaller, which is exactly what English does with 'just' or 'a bit': 'could I just have some water'. It has become so automatic that it softens requests where the amount makes no sense, such as 좀 천천히 말해 주세요, day 6's 'please speak slowly' with a little cushioning added. A bare 주세요 is not rude, but a string of them sounds like a list of orders, so when in doubt, add 좀.

Here 주세요 follows a verb instead of a noun. 포장해 and 계산해 are forms of 포장하다 'to wrap' and 계산하다 'to calculate', and adding 주세요 turns 'please give me it' into 'please do this for me'. It is the same pattern as 천천히 말해 주세요 on day 6. So 주세요 has two jobs: after a thing, 'give me'; after an action, 'do it for me'. You will learn to build those verb forms yourself on day 26, so for now take these as whole phrases.