Learn Hardcore Polish: Mój kuzyn często dzwoni do babci w niedzielę.

kuzyn = male cousin (masculine, singular) → mój kuzyn
kuzynka = female cousin (feminine, singular) → moja kuzynka
kuzyni = (mixed / all-male) cousins (masculine personal plural) → moi kuzyni

So mój kuzyn literally means my (male) cousin.

What exactly does kuzyn mean? Is it any cousin?

Yes, kuzyn is a general word for a male cousin. You don’t have to specify which side of the family.
If you need to be more precise, you can add:

kuzyn cioteczny – cousin through your mother’s or father’s sister
kuzyn stryjeczny – cousin through your father’s brother

But in everyday speech, people just say kuzyn.

What form is dzwoni and which verb is this?

The verb is dzwonić (to call / to ring, usually by phone).
dzwoni is:

3rd person singular
present tense
imperfective aspect

So Mój kuzyn dzwoni = My cousin calls / is calling.
The full present-tense paradigm is:

ja dzwonię
ty dzwonisz
on/ona/ono dzwoni
my dzwonimy
wy dzwonicie
oni/one dzwonią

Why is it dzwoni do babci and not just dzwoni babci like “calls grandma”?

In standard Polish, for phoning someone you normally say:
dzwonić do + [genitive] → dzwonić do babci = to call (phone) grandma.

The pattern is:

dzwonić do mamy – call mum
dzwonić do kolegi – call a friend (male)
dzwonić do lekarza – call the doctor

dzwoni babci is not the normal way to say “he calls grandma” in modern standard Polish. Without do, it sounds incomplete or could be interpreted as “(some bell) rings for grandma” rather than “he phones her”.

What case is babci in do babci, and what is the base form?

The base (dictionary) form is babcia (grandma), nominative singular.

do always takes the genitive case, so:

nominative: babcia
genitive: babci

That’s why the sentence has do babci.
Other examples with do + genitive:

do domu – to (the) house
do szkoły – to school
do taty – to dad

Could the sentence use a different construction like dzwoni babci with a dative?

You will sometimes see dzwonić komu? (dative) in dialects or older Polish, but for phone calls, the standard, neutral form today is dzwonić do kogo?:

dzwonić do babci – to call grandma

Using dative (dzwoni babci) in modern standard Polish sounds non‑standard or archaic for “to phone someone”. If you want to speak “textbook” Polish, stick to dzwonić do + genitive.

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

często is an adverb meaning often.

It can appear in several positions:

Mój kuzyn często dzwoni do babci w niedzielę.
Często mój kuzyn dzwoni do babci w niedzielę.
Mój kuzyn dzwoni często do babci w niedzielę.

All are grammatically correct. The most neutral is the original version, with często directly before the verb. Moving it to the beginning (Często…) puts extra emphasis on often.

Why is it w niedzielę and not w niedziela or w niedzieli?

The base form is niedziela (Sunday), nominative singular.

With days of the week meaning “on [day]”, Polish uses:
w + accusative → w niedzielę = on Sunday.

Cases here:

nominative: niedziela
accusative: niedzielę

w niedzieli would be locative and is used only in some special or literary phrases, not for the ordinary “on Sunday” meaning.

Does w niedzielę mean this coming Sunday or Sundays in general?

By itself, w niedzielę can mean either on Sunday (this/that specific one) or on Sundays in general.
In your sentence, często suggests a repeated action, so the natural reading is:

My cousin often calls grandma on Sundays (as a habit).

Context usually tells you whether it refers to one particular Sunday or a regular pattern.

Why is niedzielę spelled with ę at the end? How is that pronounced?

The ę marks the accusative form niedzielę. Historically it’s a nasal vowel.

In modern Polish, at the end of a word, ę is usually pronounced very close to plain e, so niedzielę sounds almost like niedziele.
You still must write ę because the spelling shows the correct grammatical form (accusative).

Can I change the word order, like moving w niedzielę earlier in the sentence?

Yes, Polish word order is flexible. For example, you can say:

Mój kuzyn w niedzielę często dzwoni do babci.
W niedzielę mój kuzyn często dzwoni do babci.

All of these are correct. The core grammatical information comes from endings and prepositions, not from word order. Different orders mostly change emphasis or style, not meaning.

Why is it dzwoni (imperfective) and not zadzwoni?

dzwonić (imperfective) focuses on the process or repeated actions:

Mój kuzyn często dzwoni… – he often calls (habitually).

zadzwonić is the perfective counterpart, used for single, completed events:

Mój kuzyn zadzwoni do babci w niedzielę. – My cousin will call grandma on Sunday (one specific call).

Because your sentence describes something that happens often, the imperfective dzwoni is the natural choice.