Is milk feminine?
No. It's masculine.
The verb conjugates with the subject (मैं) here. It's पिऊँगी because evidently, a woman is speaking the sentence. A man would say मैं दूध पिऊँगा।
I am currently using the "I can't listen now" option, and have the sound turned off. Sooo...
Although, I guess, it is always a woman speaking.
Both पिऊंगा and पिऊंगी should be accepted as a correct answer and you can report if it's not. You can make the choice based on your own gender.
I used piyougee; what was incorrect?
Do you mean पियोगी? That's the third-person form.
The first-person forms are पिऊँगी and पिऊँगा.
I see; okay - thank you so much. (Maybe its new distractions; I'm having a really difficult time with this section)
What is the difference between me dud peeungee and me dud peeungaa?
You should use पिऊँगी if you are female and पिऊँगा if you are male.