As vinay92 said below, the verb लेना can also mean "to buy" or "to take". Even if the word was used to mean "take". It can mean several things.
1) When the grandpa is the regular customer of Julia's dairy/ ranch and not some other dairy, such expression is used quite frequently, to denote where he gets his daily supply of milk. In the same way as "I buy bread from this bakery (often/daily)"
2) Julia (the milkmaid/milk woman) gives the daily delivery of the milk.
3) Julia (may be the wife or cook or some relative of the speaker) made him some Masala Milk (Hot milk with almonds, cardamom powder, sugar, nutmeg, etc.) and He takes it from her.
4) Julia (the neighbor) gives the Grandpa milk from her house because he didn't have any and couldn't go out to buy it.
The Hindi they're teaching in this course appears to use the "honorific plural".
This means that, to show respect, some words are treated as plural even when we are only talking about one of them.
Since you're supposed to honor your elders, "grandfather" (दादा) is treated as plural. So, "my" takes the plural form (मेरे) in order to modify it, and the verbs take the plural conjugation (लेते हैं).
Hindi is a language where respecting your elders is very important, so only very young kids will say "mummy" and "papa". After the age of about 10, you are expected to use more formal terms, such as "mother" and "father". This applies to "grandpa" and "grandfather". You might want to report it to Duolingo, because this theoretically should be accepted.
I think the reason that they didn't put "the" before "milk" is to teach there is no a "the" like word in hindi, nor is needed. It is a cup of milk or etc in english. It do exist in hindi, I am pretty sure, but it isn't necessary. When it says "my grandfather takes milk from Julia" it could be A Cup, A Bottle etc of milk. In hindi or Persian, the official language in my country, the milk itself matters, not the container.