Q1. "...a friend of mine, another college student at a different university, is a political science major. He was told by several 'reliable sources' that voters under the age of 21 do not actually vote for the President. He was told that we 18-year-old voters only participate in the election of Legislators. Also, all the hype to get teenagers to exercise their right to vote just 'conveniently overlooks' and neglects to point out the fact that our votes don't count in the Presidential election. Now, I strongly doubt these assertions, but the quality of the sources have led me to try to find textual proof of the claims."
A. The only way you could think that 18-year-olds do not vote for the President is if you stopped reading the Constitution before you get to the 26th Amendment. Oddly enough, the main body of the Constitution does not actually set an age at which people could vote. This was intentional, so that the States could set their own voting ages and other qualifications. However, the 14th Amendment does mention a voting age, for all men, of 21. This is expanded upon in the 15th Amendment (voting for all races) and the 19th (voting for women).
The 26th Amendment, however, is very clear: no one 18 or older shall be restricted from voting on account of age. It does not restrict this to Presidential elections, or any other kinds of elections. It applies to all elections.
One further point to clarify: when you vote in the Presidential elections, you are not actually casting your vote for the President, but for an elector who will vote for the President. This idiosyncrasy of the U.S. system is known as the Electoral College, and this site has a page devoted to that topic.