From a company's Income Statement, Balance Sheet, and Cash Flow data, is it possible to figure out if the company has taken out a loan and how much it has taken out?
Somewhat. The balance sheet will include liabilities which as Michael Kjörling points out would tell you the totals for the debt which would often be loans or bonds depending on one's preferred terminology. However, if the company's loan was shorter than the length of the quarter, then it may not necessarily be reported is something to point out as the data is accurate for a specific point in time only.
My suggestion is that if you have a particular company that you want to review that you take a look at the SEC filing in full which would have a better breakdown of everything in terms of assets, liabilities, etc. than the a summary page. http://investor.apple.com/ would be where you could find a link to the 10-Q that has a better breakdown though it does appear that Apple doesn't have any bonds outstanding. There are some companies that may have little debt due to being so profitable in their areas of business.