"The duck drinks the milk."
Translation:Η πάπια πίνει το γάλα.
Yes, "η πάπια" is the feminine gender noun and "το παπί" is the neutral gender. There isn't a masculine gender greek word for ducks (well, as far as I know...) and you can use them pretty much interchangeably (they don't have to match the duck's gender), though I believe you would most often find the neutral gender word to refer to younger ducks, or even ducklings.
Not always. Η γάτα (the cat) is female, το γάλα (the milk) is neutral genre, τα ποτά (the drinks) is the plural form of το ποτό (the drink) which is neutral genre. Not sure if I used the right explanation terms. You probably never see a male genre word and ending in -α unless it is a name/surname or in other grammar & syntax cases like when you use the third person. I am afraid in cases like that you have to learn if something if male, female or neutral genre by practice like you do when learning French or Italian...
Because, as in English, some times you specify that it's a known quantity of drink/food that's consumed and sometimes it's 'some':
Πίνει γάλα = drinks (some) milk
Πίνει το γάλα (που είναι στο ψυγείο) = drinks the milk that's in the fridge
Τρώει φωμί = he eats (some) bread
Τρώει το ψωμί που αγόρασε = She eats the bread that she bought