"The ball goes through the window."
Translation:De bal gaat door het raam.
It's not intuitive. You've basically got to memorize the nouns. There are some rules and general hints at https://understandingdutch.com/difference-between-de-and-het-dutch.
You have reached level 25 in German.
If a word is a der or die word in German, it is usually a de word in Dutch. De man. De vrouw. De hond. If it is a das word in German, it is usually a het word in Dutch. Het meisje. Het paard. There are exceptions. The menu is die Speisekarte in German but het menu in Dutch.
You can't compare two different words with no relation to eachother.
It only words if words are cognates, come from the same root. If you take the full dutch word. Menukaart it does work. Menu is actually only what is written on the menukaart. And often we just call it kaart.
You ask to see the menu and then you will be given de (menu)kaart. But like I said you usually simply ask to see de kaart.
No in case of a window it is het raam. It just means it's one of the (extremely) rare words where one of its other definitions takes a different article.
I myself have never come across "de raam". De raming or beraming yes but not sure it would have that meaning. I think de raam might have the same meaning as het raamwerk, the framework.