De is for both masculine and feminine words. Het is for genderless words. Words that use de are words that end on -ing and -heid for example. Words that use het are words ending on -je for example. I'm sure there are some more 'rules' here but basically you cannot know and you will have to learn and practice.
Yes and no. There is no grammatical difference between masculine and feminine nouns in Dutch. However, there are neuter nouns (just like in German) that us a different article ("het"). See here for more info on de-words and het-words. This difference does not only affect the article, but also adjectives.