Is it obligatory to return the money I took for a part of my graduation project, knowing that this part was made for free, and I falsely claimed that my father paid for it?

You are not obliged to return the money to your colleagues because you are entitled to it as compensation for your work. Your relative gifted you a part of it, making it your property, and thus it was permissible for you to exchange it for something else. However, you should not have lied. You could have used allusive speech (ma'arid), for in it there is room to avoid lying.