Not sure what you want to do but the following is something to look in to.
If you set the form's TransparencyKey property to the same colour as your form's background then the background becomes transparent and click events pass through the form to the window/object behind.
If you then set the form's BorderStyle property to None, then only the objects on the form are visible. This effect can be used to overlay one form on top of another while still having the form below clickable. However, when the form below is clicked the transparent form is sent to the back so it has limited use realy.
Also, anything drawn on the transparent form will display (provided it is not the TransparencyKey color).
Now my image has a sketchy border. How can I fix this?
Not sure about this as it depends upon your image. I am guesing that the image border (or form border) has a dithered colour (i.e. uses two or more colored pixels in a pattern to create the impression of another colour; most often found in low colour images) resulting in something like the transparent ties we used to see in the early days of TV blue screening.
Experiment with a couple of solid colour images that match and don't match the TransparencyKey to check if it is the image or the form.
I also recomend that the TransparencyKey is set to a solid primary/secondary colour (i.e. one of R G B C M Y); magenta is my favourite for a transparent background in my images.