I have 2 more questions: 1. A student who was offered a paid internship just asked if there is any vacation. My first reaction was "WTF?". Is it even appropriate to ask for vacation when you will only be working for 3 months? 2. On my job postings, I usually ask the candidate to answer 3 questions when they apply. However, more often than not, most candidates don't submit the required answers. Should I automatically discard those resumes?
I wouldn't say it's explicitly inappropriate, just a very unusual and curious question. Given this is a paid internship, I would look into your local job regulations and determine how to proceed. My first reaction was an arched eyebrow, but if it's known by the candidate that they will only be working for three months (i.e. you put it in the job ad), then it's possible they're asking because of some upcoming event they've been planning. Find out what their motivation is.
2. Unless you spot something on the resume that sticks out, stays in your mind and demands you call the person in, yes. You obviously are deriving some sort of value and introspection into your candidates by asking them these questions; it also shows basic reading comprehension and ability to follow directions.