Unfortunatley, the AdWords API isn't as open as you might think: It's meant for ad agencies managing large accounts, or software vendors who want to build ad management platforms. You need to apply to Google for an API key to gain access; they used to give them out to nearly anyone with an account, and it took about 14 days to process the application. However, Google has got very strict about their terms and conditions over the past 12 months, and to put it simply, you probably won't meet them if you're building an SEO tool; even if you apply to build a full platform, you'll need to wait six to ten weeks for approval as they've got a huge backlog of applications to process at the moment.
As this is just a student project, you should actually be able to get away with just using the AdWords API sandbox, which is open to anyone with a Google account. This won't give you real keywords or stats, but would demonstrate your understanding of the platform.
Another option would be to check out the Ad Intelligence Service of the adCenter API; you'd still need to open an adCenter account (with a $5 activation fee), but you should be able to get an adCenter API key without waiting too long. The stats available from Microsoft won't be as extensive as what Google has to offer, but will still be relevant to the at least the US market. Also, being Microsoft, they've got a good range of C# examples.