Την Κυριακή το πρωί πηγαίνω στην εκκλησία με τη γιαγιά μου.

Την is the feminine accusative singular definite article (τη(ν)). In Greek, time expressions like on Sunday / on Monday / on Friday are often expressed with the day in the accusative with the article:

• Την Κυριακή = on Sunday (literally the Sunday in accusative, used adverbially for time).
  So την doesn’t mean her here; it marks a time phrase.

Greek commonly uses article + accusative for “on + day” (and for some other time expressions), without a separate preposition:

• Τη Δευτέρα = on Monday
• Την Κυριακή = on Sunday
  You can sometimes see alternatives, but this is the most natural everyday pattern.

το πρωί means in the morning / in the morning time. Greek often uses the definite article with parts of the day:

• το πρωί = in the morning
• το βράδυ = at night/in the evening
  Here it specifies when on Sunday: Sunday morning.

In Modern Greek, the present tense can cover both habitual and current actions depending on context:

• πηγαίνω στην εκκλησία can mean I go to church (regularly) or I’m going to church (now/soon).
  With Την Κυριακή το πρωί, it typically reads as a regular habit: On Sunday morning I go to church…

στην is a contraction of σε + την:

• σε την εκκλησία → στην εκκλησία
  This is extremely common in speech and writing. It means to/in the church; context decides whether it’s destination (to church) or location (in church).

After σε/στη(ν), the noun is in the accusative:

• (σε/στην) εκκλησία = accusative singular
  So εκκλησία is accusative here because it’s the object of the preposition σε (in its contracted form στην).

Both exist, but τη is a very common shortened form of την before many consonants in everyday Greek:

• με τη γιαγιά μου = with my grandmother
  You’ll also see με την γιαγιά μου, which is more “full”/careful. The ν in την is often dropped unless it helps pronunciation (especially before vowels and certain consonants).

In Greek, possessive pronouns like μου (my), σου (your), του/της (his/her), typically come after the noun:

• η γιαγιά μου = my grandmother
  Putting it before (μου η γιαγιά) is not the normal neutral pattern (it can occur in special/emphatic structures, but it’s not the default).

Greek stress is shown with the accent mark and is important:

• Την Κυριακή (kee-ree-a-KEE)
• το πρωί (pro-EE)
• πηγαίνω (pee-ye-NO)
• στην εκκλησία (stin ek-klee-SEE-a)
• με τη γιαγιά μου (me tee ya-YA moo)
  Also note γιαγιά: the γ before ι/ε is pronounced like a soft “y” sound for many learners (closer to ya- than a hard g).