Η μαμά μου μού είπε να πάρω γάλα, αυγά και βούτυρο.

They are two different uses of the same weak pronoun:

• μαμά μου = my mom → μου is possessive (my) after the noun.
• μού είπε = told me → μού is an indirect object pronoun (to me).

So the sentence contains both my (possession) and me (recipient).

Yes, these follow typical Greek placement rules:

• Possessive weak pronouns (like μου) commonly come after the noun: η μαμά μου.
• Object weak pronouns (like μου/μού) usually come before the verb: μού είπε.

You can use stronger/emphatic forms or different word orders for emphasis, but this is the most neutral/natural pattern.

να introduces a clause in the subjunctive pattern (often used for commands, requests, purpose, etc.). After verbs like λέω (in the sense of tell/ask), Greek commonly uses:

• (μου) είπε να + verb = (she) told me to + verb

So μού είπε να πάρω… = she told me to get/buy…

Greek often omits articles when listing groceries/materials in a general “some X” sense:

• να πάρω γάλα, αυγά και βούτυρο = to get (some) milk, eggs, and butter

You can add articles for specificity (e.g., το γάλα = the milk, a specific one), but the bare nouns are very common for shopping lists.

They are direct objects in the accusative:

• γάλα: neuter singular (same form in nominative/accusative)
• αυγά: neuter plural (same form in nominative/accusative)
• βούτυρο: neuter singular (same form in nominative/accusative)

Neuter nouns often have identical nominative and accusative forms, so you rely on sentence structure/function.