If you are trying to reach students by guessing keywords like "homework" for your AdWords campaign, you may want to reconsider whether it is money well spent. This site, for example, does not mention "homework" once.
I honestly can think of no better way to precisely reach high school and college students than through a resource they will need to do their homework for a class required by every high school and college in the world.
Expect at minimum (except for around Christmas and at the beginning of summer) fifty thousand views of your message per day. In the peak of the fall and spring semesters, expect 100,000 visits on weekdays, with 85% of those being unique people.
Absolutely. It's trivial to ensure any number of conditions are met using the AdWords targeting interface. How about only targeting Australian students? How about only showing your message to lazy students who are doing their homework after midnight their local time? Perhaps you only want to reach college students living in a dorm? Perhaps only students at Stanford? You can even combine restrictions, such as only British students who found this page through Google and are visiting Sunday night.
Set your AdWords bid as high or low as you like. You will always pay the least amount possible for the position thanks to Google's realtime bidding system. Think of it as eBay for ads. No matter how high you bid, you'll never pay more than enough to beat the highest bidder. Compare the price to taking out an ad in a college newspaper for a day. At a huge college, maybe 10,000 people will see your message…for how much?