Is there a way to draw/create polygons on chart to show, for example, noise sensitive areas near one's home airfield?

Sort of. You can use the Data Creator application shipped with SkyDemon Plan to create your own airspace definitions. We can't give you instructions on how to use it, because it isn't a supported part of the product, but you can still use it. You can then save your custom aeronautical data to the cloud and open it again on your devices too.