Did the Battle of Britain actuallly change the course of the war? If it did, does this mean that it helped to secure victory for the allies?
No, the Battle of Britain didn't by itself change the course of the war. It did however help to prevent the invasion and occupation of Britain, which meant that Britain continued to be like a gigantic aircraft carrier perminantly moored off the north coast of Europe.
Hitler had earlier ordered the destruction of the RAF airbases in the south of England as a prelude to invasion. He nearly succeeded but was taken in by egotistical and corrupt reports from the German airforce about it's successes. Hitler then switched from attacking the RAF to blanket bomb London and other cities. This gave the RAF time to regroup, restaff and come up with a strategy to best use the advantages their planes (spitfire and hurricane) gave them over the German planes and air battle strategies.
Hitler was very suprised when his airforce started to get a hammering and he was very conscious that he needed to save his planes for the fighting on the Eastern Front which had just got viscious. So he sent massive numbers of planes in a sustained short burst to eliminate what he thought was all that was left of the RAF (ie the Battle of Britain). He called off his planes when he realised that the losses were exceeding the potential advantage gained and instead looked east where the bigger problem lay.
The Battle of Britain therefore marked a turning point in Hitler's fortunes, and kept a base open (England) for the Allies from which they could later stage an invasion of German occupied lands and attack him in force whilst the Russians slaughtered their way in from the East. It was this stretching out of Hitler's army on different fronts thousands of miles apart that caused his defeat.
Go to the library, and check out this book:
"Fighter: The True Story of the Battle of Britain" by Len Deighton. It's a good place to start looking for answers to your questions, which I assume are for a homework assignment. He talks a lot about the aftermath of the battle, and it's impact on the overall course of the war, including an interesting section on how it shaped U.S. public opinion.