YES BUT TURN OFF THE FRICKIN’ WATER BEFORE TAKING IT APART

It appears to be LG Himacs or Corian synthetic solid surface. Basically hard plastic. “If it is”, it can be sanded and buffed to the desired sheen. I’d look for an experienced person to do this so it comes out uniformly. I had LG and it looked best when i used stainless steel spray polish, basically mineral oil, which hid the scratches. The benefit of this solid surface, is that it can be rejuvenated and repaired invisibly. But prone to gouges and scratches. If it’s a soft stone it can probably be buffed by a pro…

Look for the door in the Masonite catalog. Or find a local door/millwork supply and find out the brand they carry. Hollowcore styles are very common and can be ordered. The more common ones were well under $100. They can hinge match the mortises from the old door and you just take it home and pop in the hinge pins. If your door is as beat as it sounds, I'd drop a c-note rather than fixing it.