"Does she order a hamburger?"
Translation:그녀는 햄버거를 주문하니?
I was confused about 주문하다 and 시키다. Here's what I found.
주문하다 - To order. 주문하겠습니다? Are you ready to order? 이거는 안 주문했어요. I didn't order this.
시키다 - To order, to make someone do something. 햄버거를 시켰어요. I ordered a hamburger. 내 딸에게 영어 공부를 시켰어요. I ordered my daughter to study English.
The difference is in the social position of the speaker. 시키다 seems like you are talking about someone lower in social position than you or who you have some authority over. (e.g., employee, student). Despite having higher social position than a restaurant worker, you would still use 주문하다.
There's also 명령하다 which means to command, order, or instruct.
You can read more here: http://koreanselfstudyisntlame.blogspot.kr/2010/08/vs_29.html