I need to make the same curve as the picture from scratch in PS, using Gaussian Blur > Dissolve > Bitmap (50% Threshold). The other way I made the vector curve to Shadow > Dissolve > Bitmap. However, both methods don't have the same noise effect with the picture. Do you guys have any other suggestion?
That is not "noise" it is a Diffusion Dither.
Use the same procedure as your case 1, but choose Diffusion Dither instead of 50% Threshold.
Play with the resolutions and scales. Also play with the curves in your original image to achieve more or less dither.