To make the rotating square move slower, you can decrease the value of the `angle` variable increment in the `while` loop. For example, you can change the line `angle += 0.01` to `angle += 0.005` to make the square rotate slower.

To change the color of the square as it rotates, you can define a function that takes the current angle as an argument and returns a color based on that angle. For example, you can define a function like this:

```python
def get_color(angle):
    red = int((1 + math.sin(angle)) * 128)
    green = int((1 + math.sin(angle + math.pi / 2)) * 128)
    blue = int((1 + math.sin(angle + math.pi)) * 128)
    return (red, green, blue)
```

This function uses the `sin` function from the `math` library to calculate the values of the red, green, and blue color components based on the current angle. The values are scaled to be in the range of 0 to 255, and then returned as an RGB tuple.

To use this function to draw the square with a changing color, you can replace the line `pygame.draw.polygon(screen, BLACK, [rotated_corner1, rotated_corner2, rotated_corner3, rotated_corner4])` with:

```python
color = get_color(angle)
pygame.draw.polygon(screen, color, [rotated_corner1, rotated_corner2, rotated_corner3, rotated_corner4])
```

This will change the color of the square as it rotates based on the `get_color()` function.
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