You are trying to run a 10" duct system to a low vs more common higher output termination. I think with the correct power remote exhaust fan it can work. Calculate losses from elbows and length. Makeup air will need to be configured anyway. Induction will require less of both. I see your other question about rectangular duct. I'd pursue that.

I have no idea lets sees the layout I usually like ranges on exterior walls where venting can usually be handled . I certainly would not do what you are asking since 2 very different types of venting . Downdrafts are honestly close to useless so post a bit more info This is why you do not do duplicate posts on the same subject /

Yes, it would be best if OP showed (photos) and explained the situation and layout. Too little information provided, to get useful answers. For all we know, the old downdraft might use a 4” duct.

What do you means "space in the ceiling"? You don't need ceiling space. You just run the duct up and out the roof. You can change from round to square to create a chase if there's an upper floor, or do a 90 and run it through the joists to the exterior. Or flat on top of the cabinets to the exterior, hidden by crown. There's a dozen different ways to vent properly. And NONE involve a downdraft.