Re: When I export a PNG file on illustrator, I get random empty space along with my exported object. Is there any way I can make just my object export and nothing more?

You can try to select the background rectangle and choose: Object > Artboards > Fit to Selected Art.

Then select the Use Artboards checkbox when exporting.

But even then you will risk to see a tiny semi- transparent edge if the background rectangle and the artboard have fractional pixel values.