Look at your definition of Class1:
Form1 obj = new Form1();
This constructs a new instance of the Form1 object, which you then modify.
Since this is contained within the class, it does not affect the instance outside (which contains the class1 instance).
This is difficult to explain without pictures, but I'll try:
What you are trying to do is have a car (Form1). Inside the car, is a glove box (Class1). When you open the glove box (via the button1_click event) you create a new car and repaint it. You then close the glove box, and expect the original car to be a different colour.
Find a book on C#. An elementary one, and read the chapter on instances. You need to understand this stuff in good detail before you go any further, as nothing will make sense until you do!
Good luck.