I'm a little confused with this sentence ("Piję mleko"). I trust that the correct translation is "I am drinking milk", but that is the same translation for "Ja pije mleko".
Does the e-ogonek convey the "I"? Such that "Piję " means "I am drinking ", and "Pije" means "drinks/is drinking".
Yes, I'm having difficulty distinguishing between pije and piję, though I know the difference in meaning. Perhaps using good headphones will help, since the differences between some vowel sounds is very subtle.
Not exactly but really good thinking, the "ę" with the ogonek is a completely different letter than "e". The verb Pić (to drink) always conjugates to Piję when you want to say (I drink), regardless if the pronoun 'Ja' is present or not.
Both translations (Ja piję mleko) or (Piję mleko) should be accepted. The conjugation is unique to the first person singular, 'Ja'. So there isn't a great need to include 'Ja' since it's already implied. :)