Learn Hardcore Polish: To zdjęcie z wakacji nad morzem jest dla mnie miłym wspomnieniem i poprawia mi humor. - This photo from holidays by the sea is a nice memory for me and improves my mood.

Also, when you put a demonstrative directly before a noun like this (to zdjęcie, ta książka), it’s more like an adjective (this photo, that book), not the standalone to jest… structure (this is…).

What exactly does z wakacji nad morzem modify? Is it all describing zdjęcie?

Yes. The whole chunk z wakacji nad morzem is an extended modifier of zdjęcie:

zdjęcie z wakacji – a photo from (my) holidays
wakacji nad morzem – holidays at the seaside / by the sea

So structurally:

To zdjęcie [z wakacji [nad morzem]]…
- zdjęcie (photo)
- z wakacji (from holidays)
- nad morzem further describes wakacji: holidays which took place at/by the sea.

A natural English rendering is: This photo from my seaside holiday…

Why is it z wakacji and not z wakacje or z wakacjami?

Because of two things: the preposition z and the noun wakacje.

z can mean:
- from (a place, time, event) → it takes the genitive,
- with (together with someone/something) → it takes the instrumental.
wakacje is a plural-only noun:
- Nominative: wakacje
- Genitive: wakacji
- Instrumental: wakacjami

In this sentence, z means from (from the holidays), so it must be followed by the genitive:

z wakacji = from (the) holidays

If you said z wakacjami, that would suggest with the holidays, which doesn’t make sense here.
z wakacje is simply ungrammatical: wrong case.

Why is it nad morzem and not nad morze or na morzu?

The choice depends on meaning and case:

nad morzem (with morzem = instrumental)
- Used with location: being at/by the sea.
- Jestem nad morzem. – I am at the seaside.
- In the sentence: wakacje nad morzem = holidays at the seaside.
nad morze (with morze = accusative)
- Used with movement towards: going to the seaside.
- Jadę nad morze. – I’m going to the seaside.
na morzu (with morzu = locative)
- Means on the sea, usually on the surface (e.g. on a boat, at sea).
- Statek jest na morzu. – The ship is at sea / on the sea.

Here we are talking about where the holidays took place (location at the shore), so nad morzem is correct.

What case is miłym wspomnieniem, and why do we use that case after jest?

Miłym wspomnieniem is in the instrumental case.

Base forms:
- miłe wspomnienie – a nice memory (nominative)
Instrumental singular:
- neuter noun: wspomnieniem
- adjective: miłym

In Polish, when you say X is Y and Y is a noun phrase that classifies or describes X, you very often use the instrumental after być (jest, są, etc.):

Ona jest lekarką. – She is a doctor.
To jest problemem. – That is the problem.
To zdjęcie … jest miłym wspomnieniem. – This photo is a nice memory.

You can sometimes hear nominative (To zdjęcie jest miłe wspomnienie) in colloquial speech, but instrumental is the standard, correct form here.

Could I say To zdjęcie jest dla mnie miłym wspomnieniem z wakacji nad morzem instead? Is the word order important?

Yes, you can say:

To zdjęcie jest dla mnie miłym wspomnieniem z wakacji nad morzem i poprawia mi humor.

This is perfectly correct. Polish word order is fairly flexible. Moving dla mnie or z wakacji nad morzem around doesn’t usually change the core meaning, just the focus or what sounds more natural.

Some options that work:

To zdjęcie z wakacji nad morzem jest dla mnie miłym wspomnieniem… (original)
To zdjęcie jest dla mnie miłym wspomnieniem z wakacji nad morzem…
To zdjęcie z wakacji nad morzem jest miłym wspomnieniem dla mnie… (a bit more emphasis on dla mnie)

All of these are grammatical; the original one is very natural.

Why do we have both dla mnie and mi in the same sentence? Aren’t they the same thing?

They are related but not the same; they’re different grammatical roles:

dla mnie:
- dla = for
- mnie = genitive form of ja (here after dla)
- Meaning: for me, in my opinion / from my perspective.
- In jest dla mnie miłym wspomnieniem → it is a nice memory for me (personally).
mi:
- Dative form (unstressed variant) of ja.
- In poprawia mi humor → literally it improves mood to me = it improves my mood, it cheers me up.
- Here mi marks who is affected by the action.

So:

dla mnie = for me (as a beneficiary / from my point of view).
mi = to me (indirect object: whose mood is being improved).

What’s the difference between mi and mnie in poprawia mi / mnie humor?

Both are dative forms of ja, but they differ in stress and position:

mi:
- Unstressed clitic form.
- Typically used inside the sentence, close to the verb:
  - On zawsze mi pomaga.
  - To zdjęcie poprawia mi humor.
- Sounds natural and neutral here.
mnie:
- Stressed form.
- Used when you want to emphasize me (contrast with someone else) or when the pronoun stands alone or at the beginning:
  - Mnie to nie interesuje. – I am not interested (but maybe others are).
  - To poprawia humor mnie, nie tobie.

In your sentence, poprawia mi humor is the most natural choice.
Poprawia mnie humor would be understood, but it sounds unusual or very strongly emphasized and is not what people normally say.

Why is it humor, not humoru or humorem after poprawia?

Because humor is the direct object of the verb poprawia (improves), and the direct object usually takes the accusative case.

For humor (a masculine inanimate noun), nominative and accusative are the same:

Nominative: humor
Accusative: humor
Genitive: humoru
Instrumental: humorem

So in:

To zdjęcie poprawia mi humor.

we have:

poprawia (verb)
mi (indirect object, dative)
humor (direct object, accusative)

Using humoru (genitive) or humorem (instrumental) here would be wrong.

Can I also say To zdjęcie poprawia mój humor instead of poprawia mi humor? Is there a difference?

Yes, you can say both:

To zdjęcie poprawia mi humor.
To zdjęcie poprawia mój humor.

Both mean essentially This photo improves my mood / This photo cheers me up, but there’s a nuance:

poprawia mi humor:
- Very idiomatic and common.
- Literally improves mood to me.
- Focus is on the effect on you as an indirect object.
poprawia mój humor:
- More literal: improves my mood.
- Slightly more explicit possessive, but not as idiomatic as the dative version in everyday speech.

In practice, people use poprawia mi humor more often in this type of emotional context.

Could we also say To zdjęcie z wakacji nad morzem jest dla mnie miłym wspomnieniem i poprawia mi się humor? What’s the difference?

Yes, that is possible, but the focus changes slightly:

poprawia mi humor:
- Verb poprawia (improves) with direct object humor.
- Structure: it improves my mood.
- The subject (to zdjęcie) acts directly on your mood.
poprawia mi się humor:
- się makes the verb reflexive.
- humor becomes the subject: my mood improves.
- Literally: my mood is improving (to me).

So:

To zdjęcie poprawia mi humor. – This photo improves my mood / cheers me up.
To zdjęcie… poprawia mi się humor. – When I see this photo, my mood improves.

Both are fine, but the original is simpler and very natural.

What aspect and tense is poprawia, and how would the sentence change with poprawi?

Poprawia is:

Imperfective aspect
3rd person singular, present tense of poprawiać.

In this sentence, it suggests:

a general, repeated effect or
a current effect: this photo (whenever I look at it) improves my mood.

If you used the perfective poprawi (from poprawić):

To zdjęcie z wakacji nad morzem jest dla mnie miłym wspomnieniem i poprawi mi humor.

then:

poprawi is perfective, so it refers to a single, completed improving in the future.
It sounds more like a promise or prediction: it will improve my mood (on that occasion).

In your original sentence, the idea is more habitual / general (this photo tends to cheer me up), so poprawia is the natural choice.