For your reference, Here are the IRC Code regarding Hood range:

M1503.1 General. Range hoods shall discharge to the outdoors through a single-wall duct. The duct serving the hood shall have a smooth interior surface, shall be air tight and shall be equipped with a backdraft damper. Ducts serving range hoods shall not terminate in an attic or crawl space or areas
inside the building.
Exception: Where installed in accordance with the manufacturer’s installation instructions, and where mechanical or natural ventilation is otherwise provided, listed and labeled ductless range hoods shall not be required to discharge to the outdoors.

As for the height requirement above the cooktop the IRC states the following.
SECTION G2447 (623)
COOKING APPLIANCES
G2447.1 (623.1) Cooking appliances. Cooking appliances that are designed for permanent installation, including ranges, ovens, stoves, broilers, grills, fryers, griddles, hot plates and barbecues, shall be tested in accordance with ANSI Z21.1 or ANSI Z21.58 and shall be installed in accordance with the manufacturer’s installation instructions.
G2447.5 (623.7) Vertical clearance above cooking top.
Household cooking appliances shall have a vertical clearance above the cooking top of not less than 30 inches (760 mm) to combustible material and metal cabinets. A minimum clearance of 24 inches (610 mm) is permitted where a hood is installation.

It is my advice that you check with your local authority jurisdiction. They often set respective guidelines which can supersede IRC.