Learn Hardcore Polish: Czuję dużą dumę z córki i ta emocja pomaga mi w pracy. - I feel great pride in my daughter and this emotion helps me at work.

In Polish, czuć normally takes its object in the accusative case.
The noun duma (pride) in singular accusative is dumę, and the adjective duży must agree with it in case, gender, and number, so:

nominative (dictionary form): duża duma – big pride (as a subject)
accusative (after czuję): dużą dumę – I feel big pride

So:

Duża duma pomaga mi w pracy. – Big pride helps me at work. (subject → nominative)
Czuję dużą dumę. – I feel big pride. (object → accusative)

Why is it z córki and not z córkę or z córką?

The preposition z here means “of / about / in (someone)” in the sense of being proud of someone, and it requires the genitive case.

The noun córka (daughter) declines like this (singular):

nominative: córka – subject form
genitive: córki – after z in this meaning
accusative: córkę
instrumental: córką

The pattern is:

duma z kogo? z czego? → genitive
- duma z córki – pride in/of (my) daughter
- duma z syna – pride in (my) son
- duma z osiągnięć – pride in achievements

So z córki is genitive singular, which is required by duma z kogoś.

What exactly does z córki mean? Is it “with my daughter” or “from my daughter”?

Literally, z often means from / with, but in this fixed pattern it corresponds to English “of / in / about” in the emotional sense:

duma z kogoś = pride in someone / pride about someone

So:

Czuję dużą dumę z córki. ≈ I feel great pride in my daughter / I’m very proud of my daughter.

It does not mean:

with my daughter (that would be z córką, using instrumental)
from my daughter as in I receive pride from her (Polish would express that differently)

This is just how Polish expresses being proud of someone:
być dumnym z kogoś, czuć dumę z kogoś.

Where is the word “my” in this sentence? Why isn’t it z mojej córki?

Polish often omits possessive pronouns (my, your, his, etc.) when the owner is obvious from context, especially with close family members.

So:

z córki – usually understood as of my daughter when I am speaking about my own life
z mojej córki – of my daughter, explicitly emphasizing it is my daughter, not someone else’s

Both are grammatically correct. Native speakers tend to use the shorter form when the possessor is clear, just like:

Idę do mamy. – I’m going to (my) mom.
Rozmawiałem z bratem. – I talked with (my) brother.

Why is it ta emocja, and not ten emocja or to emocja?

The noun emocja (emotion) is feminine in Polish.

Demonstrative pronouns (this/that) must agree in gender, number, and case with the noun:

masculine: ten (ten chłopiec – this boy)
feminine: ta (ta emocja – this emotion)
neuter: to (to dziecko – this child)

So:

ta emocja – this emotion (correct, because emocja is feminine)
ten emocja, to emocja – incorrect with this noun

If you changed the noun, the pronoun would change:

to uczucie – this feeling (because uczucie is neuter)
ten stan – this state (because stan is masculine)

Why is it mi and not mnie in ta emocja pomaga mi w pracy?

Both mi and mnie are forms of me in the dative case (to/for me), which is required by pomagać:

pomagać komu? czemu? → dative
- pomaga mi – it helps me
- pomaga tobie – it helps you

The difference is style/emphasis:

mi – short, unstressed form, usually used inside the sentence:
- Ta emocja pomaga mi w pracy.
mnie – longer, stressed form, used for emphasis or at the beginning/end:
- Ta emocja pomaga mnie, a nie jemu.
- Mnie ta emocja pomaga w pracy.

In your neutral sentence, mi is the natural choice.

Why is it w pracy and not na pracy?

For “at work / at my job”, Polish normally uses:

w pracy – literally in work, idiomatically at work

This is w + locative case:

w pracy – in/at work
w domu – at home
w szkole – at school
w biurze – at/inside the office

Na pracy is not used in this meaning. Na + locative is used for many other places/events (na dworcu, na uczelni, na spotkaniu), but praca specifically takes w for “at work”.

So:

Ta emocja pomaga mi w pracy. – This emotion helps me at work. ✅
Ta emocja pomaga mi na pracy. – incorrect in standard Polish.

Could I say Czuję się dumny z córki instead? What’s the difference?

Yes, you can, and it’s very natural. The nuance is slightly different:

Czuję dużą dumę z córki.
- Focuses on the feeling as a noun: I feel a great amount of pride in my daughter.
- More abstract, emphasizes the emotion itself.
Czuję się dumny z córki.
- czuję się + adjective: I feel proud of my daughter.
- Describes your state (you being proud) rather than the “quantity of pride”.

Both are correct. In everyday speech, Czuję się dumny z córki or simply Jestem dumny z córki is more common; czuję dużą dumę z córki sounds a bit more formal or reflective.

Why is the conjunction i used here? Could it be a?

Both i and a can translate as “and”, but they differ slightly:

i – neutral “and”, just joining similar things:
- Czuję dużą dumę z córki i ta emocja pomaga mi w pracy.
  Two related facts about the same thing.
a – “and/but” with a sense of contrast or slight opposition:
- Czuję dużą dumę z córki, a ta emocja czasem mi przeszkadza.
  I feel great pride in my daughter, and this emotion sometimes bothers me. (contrast)

In your sentence, you’re just adding information (no contrast), so i is the natural choice. A would sound like you’re contrasting two situations.

Why is the verb pomaga in the present tense if this is a general, ongoing effect?

In Polish, the simple present tense is used both for:

what is happening right now
what happens regularly / generally

So:

Ta emocja pomaga mi w pracy.
= This emotion helps me at work (in general, habitually).

There is no separate form like English “helps / is helping / tends to help”; context shows it’s a general truth. This is completely normal and correct.

Is it okay to include ja and say Ja czuję dużą dumę z córki…?

Grammatically yes, but stylistically it’s usually unnecessary.

The verb ending -ę in czuję already tells us the subject is “I”, so:

Czuję dużą dumę z córki. – natural, neutral
Ja czuję dużą dumę z córki. – adds emphasis on I specifically

Use Ja when you want to contrast or stress:

Ja czuję dużą dumę z córki, a on czuje tylko zazdrość.
I feel great pride in my daughter, but he feels only jealousy.

In a simple, neutral statement, native speakers would typically omit ja.