Just a little hint: a lot (not all!) of german nouns ending on "-e" are female. for instance: Brücke (bridge), Blume (flower), Lampe (lamp), Liste (list), Ruhe (silence). But on the other hand a lot of nouns describing the member of an ethnic group ending on "-e" are the male versions: "der Däne" (the danish man), "der Ire" (the irish man), "der Portugiese" (the portuguese man" and so on.
Also all the nouns ending on the suffixes "-heit", "-keit", "-schaft" and "-ung" are female.
First of all you're right about the "-heit", "-keit", "-schaft", "-ung" thing.
But for the "-e" I only can say: be careful with such "rules". They won't help you, as there are so many words ending in "-e" which are not feminine.
(And, of course, talking about grammatical gender you use "feminine" and "masculine", not "female" and "male", as e.g. "Mädchen" is female, but it's not feminine.)
Nouns for objects ending in -e are practically all feminine. Only exceptions i am aware of are Auge and Käse.
EDIT: Can't reply to the next comment, so here. Read my comment again. All OBJECTS (things: dead stuff you can touch) ending in -e are feminine. Only two objects in your list: das Gebirge/Gemüse, because Ge- takes precedence here. So, once you know the rule, a great help.
sarefo, there are many more:
masculine: der Bürge, der Türke, der Junge, der Zeuge, der Name, der Glaube, der Wille, der Gedanke, der Junge, der Kollege, der Kunde, der Experte...
neuter: das Ende, das Interesse, das Gebirge, das Gemüse...
Basically: If you have to guess, choosing "feminine" for a noun ending in "-e" is a good idea. But it's not that useful as a strict rule.
This may sound critical, and I don't mean it to, but the best way to find the links is to do the searches yourself. That way you can find the one that presents the information in the easiest format for YOU to understand. There is so much information out there that it doesn't take much to word a search to get your answer. I am certainly not saying that this discussion isn't extremely valuable. It is priceless. But it's greatest value is not to simply answer grammar questions but provide more practical real world advice about the more subtle aspects of German. So read through the comments, but also take an opportunity to do a little "research" yourself. Working for it a little more generally translates into greater retention as well.
I don't know how far Duo has come with their light bulb system. I do the vast majority of my practice on my Android phone which never had much help. But now in my Spanish course they do have the light bulb on the start pop-up along with start and the option to test out of the level. But I also take German, French, Italian, Portuguese and Dutch on Duo and I haven't seen a light bulb in any of those.
There are three genders in German and four cases. With plural acting almost like a fourth gender, case markers can get complex. Here is a basic overview of cases in German
Below are the complete declension tables. You will need those for a while probably.
The only real system for determining gender in German is memorizing a lot of endings that determine the gender, and that system is far from perfect. In German, like in most gendered languages, the best system is always to learn the article when you learn the noun. Don't just learn Suppe means soup, learn die Suppe. But the great percentage of nouns ending in e are feminine. The German word for girl, das Mädchen, is neuter because it ends in chen. But you also have to remember to learn how each nouns forms its plural. Again there are some ways to predict, but again there's a lot of individual cases. So again I recommend learning that when you learn the noun. Once you learn the rather complex set of determines you need to at least confirm that the word obeys one of the rules you know when you learn it.
This article discusses the various endings associated with the three German genders.