Basically you should not exceed 1000 feet per minute after you have passed the initial approach fix. The actual rate of descent will vary with speed, the approach angle and type of approach as well as met conditions. Please see this article.
In the USA the maximum rate would only be that considered safe and in control for the equipment, crew training, and conditions. Decent angles are fixed to the ground and not aircraft vertical or horizontal airspeeds or relative airflow angle.
Each segment of an approach has different slope and clearance requirements as they expect different aircraft ...
The grey areas are the minimum descent altitude (MDA) for each approach segment. Below those altitudes there are hazards in those segments. When you conduct the approach you should be aware of those altitudes and take action if you get too close to them.