Learn Hardcore Greek: Ρωτάω συχνά τη γιαγιά μου για την ηλικία της και για την παιδική της ζωή. - I often ask my grandmother about her age and about her childhood.

ρωτάω means I ask (a question).
ρωτώ is essentially the same verb; it is a slightly more formal or slightly older-sounding variant. In everyday speech, ρωτάω is more common.

Do not confuse ρωτάω (ask a question) with ζητάω (ask for / request).

Ρωτάω τη γιαγιά μου = I ask my grandmother (questions).
Ζητάω από τη γιαγιά μου χρήματα = I ask my grandmother for money.

Why is there no word for I (like εγώ) in the Greek sentence?

Greek usually drops subject pronouns because the verb ending already shows the subject.
Ρωτάω is first person singular, so it already means I ask.

You use εγώ mainly for emphasis or contrast:

Εγώ ρωτάω συχνά τη γιαγιά μου… = I (as opposed to someone else) often ask my grandmother…

Why is it τη γιαγιά μου and not something like στη γιαγιά μου?

The verb ρωτάω takes a direct object in the accusative case, without a preposition:

ρωτάω κάποιον κάτι = I ask someone something.

So τη γιαγιά μου is accusative: (εγώ) ρωτάω τη γιαγιά μου.
Using στη γιαγιά μου would mean to my grandmother and would be wrong with ρωτάω in standard Greek.

Why do we need the article τη before γιαγιά μου?

In Greek, possessives like μου normally go together with the definite article.
So you usually say:

η γιαγιά μου (my grandmother – subject)
τη γιαγιά μου (my grandmother – object)

Leaving the article out (γιαγιά μου) is possible in some contexts (especially vocative, when calling someone: Γιαγιά μου!), but for normal sentences the article is standard.

Why is it τη γιαγιά but την ηλικία? What’s happening with that final -ν?

The weak feminine article in the accusative is την, but in everyday writing and speech the final -ν is often dropped before many consonants:

Before vowels and certain consonants (π, τ, κ, ψ, ξ, μπ, ντ, γκ, τσ, τζ) we usually keep the -ν.
Before most other consonants, many people drop it.

So:

τη γιαγιά (γ is a consonant where dropping -ν is common)
την ηλικία (η is a vowel, so we keep -ν)

Both τη and την are grammatically the same form; the -ν is mainly a pronunciation/spelling convention.

What does συχνά mean, and where can it go in the sentence?

Συχνά means often. In this sentence:

Ρωτάω συχνά τη γιαγιά μου… = I often ask my grandmother…

You can also move it a bit:

Συχνά ρωτάω τη γιαγιά μου…
Ρωτάω τη γιαγιά μου συχνά…

All are possible. The most neutral positions are either right after the verb or at the very beginning of the sentence.

Why is the preposition για repeated: για την ηλικία της και για την παιδική της ζωή? Could we omit the second για?

Yes, you can omit the second για:

…για την ηλικία της και την παιδική της ζωή.

Repeating για is stylistic: it adds a bit of clarity and rhythm, and is quite common in speech and writing.
Both versions are correct and natural:

για Α και Β
για Α και για Β

What does για mean here, and which case does it take?

Here για means roughly about:

ρωτάω για κάτι = I ask about something.

Για always takes the accusative:

για την ηλικία (accusative)
για την παιδική της ζωή (accusative)

So the nouns after για are in the accusative case.

What exactly does ηλικία mean, and what gender is it?

Ηλικία means age (as in how old someone is).
It is a feminine noun: η ηλικία.

In the sentence για την ηλικία της, it is in the accusative singular feminine (because of για):

nominative: η ηλικία
accusative: την ηλικία

What is της in την ηλικία της and την παιδική της ζωή?

Της here is the weak possessive pronoun her.
It is genitive singular feminine (also used for its in many contexts).

την ηλικία της = her age
την παιδική της ζωή = her childhood (literally: her childish life)

The normal placement is after the noun: η ηλικία της, η ζωή της.

Why is it παιδική ζωή and not just παιδιά ζωή?

Παιδική is an adjective meaning childish / child / of childhood, formed from παιδί (child).
Παιδική ζωή literally means childish life, i.e. childhood.

You do not say παιδιά ζωή; that would be like saying children life in English. Greek, like English, uses an adjective-like form here:

English: childhood, childish
Greek: παιδική ζωή

Why is the adjective παιδική in the feminine form?

Παιδική agrees with ζωή, which is a feminine noun: η ζωή (life).
Adjectives in Greek must agree with the noun in gender, number, and case.

So here we have:

feminine noun: ζωή
feminine singular accusative adjective: παιδική
→ την παιδική ζωή (and with the possessive: την παιδική της ζωή).

Is the word order την παιδική της ζωή fixed, or can we move της?

The usual, natural order is την παιδική της ζωή (article – adjective – possessive – noun).
Other orders like την παιδική ζωή της or τη ζωή της την παιδική are possible but sound more marked, poetic, or emphatic.

For everyday speech, keep:

την ηλικία της
την παιδική της ζωή

Could we replace τη γιαγιά μου with a pronoun, like την?

Yes. Once it’s clear who you are talking about, you can use a clitic object pronoun:

Τη ρωτάω συχνά για την ηλικία της… = I often ask her about her age…

Here την (or τη) stands for τη γιαγιά μου.
Clitic pronouns normally come right before the verb in the present tense.

Is the tense ρωτάω here talking about a habit (I often ask) or something happening right now?

The Greek present tense covers both:

a general habit: Ρωτάω συχνά τη γιαγιά μου… = I often ask my grandmother…
something happening now: Τώρα ρωτάω τη γιαγιά μου… = I am asking my grandmother now.

In this sentence, the adverb συχνά makes the habitual meaning clear: it describes something that happens regularly.