Learn Hardcore Polish: Wieczorem czuję zmęczenie i chcę po prostu odpocząć. - In the evening I feel fatigue and just want to rest.

czuję zmęczenie
- czuję (I feel) + zmęczenie (fatigue – a noun in the accusative case)
- Literally: I feel fatigue.
- More formal or neutral, focuses on the state as a thing you experience.
czuję się zmęczony
- czuję się = I feel (myself)
- zmęczony = tired (adjective, masculine)
- Literally: I feel tired.
- Very common in everyday speech; sounds a bit more personal/subjective.

So:

Wieczorem czuję zmęczenie – In the evening, I experience a feeling of fatigue.
Wieczorem czuję się zmęczony – In the evening, I feel (that I am) tired.

Both are correct; the sentence you have simply chose the noun version.

What case is zmęczenie, and why that form?

Zmęczenie is a neuter noun meaning fatigue / tiredness.

Here it is in the accusative case, because it is the direct object of the verb czuję (to feel).

Verb: czuć (kogo? co?) – to feel (whom? what?) → takes accusative
Object: zmęczenie – fatigue

For neuter nouns, the nominative and accusative forms are usually identical:

nominative: zmęczenie (fatigue is…)
accusative: czuję zmęczenie (I feel fatigue)

So the same form zmęczenie serves as both subject (nominative) and object (accusative).

Why is there no ja (I) in the sentence?

Polish normally omits subject pronouns like ja (I) because the verb ending already shows the subject.

czuję can only mean I feel (not you/he/we, etc.)
chcę can only mean I want

So Ja wieczorem czuję zmęczenie i chcę po prostu odpocząć is grammatically correct, but:

it sounds more emphatic, like I, in particular, in the evening feel tired and want to rest.
In a neutral sentence, Polish prefers to drop ja and just say:
Wieczorem czuję zmęczenie i chcę po prostu odpocząć.

What verb is chcę, and why does it end in -ę?

Chcę is the 1st person singular present tense of chcieć (to want).

Present tense of chcieć:

ja chcę – I want
ty chcesz – you want (singular, informal)
on/ona/ono chce – he/she/it wants
my chcemy – we want
wy chcecie – you want (plural)
oni/one chcą – they want

The -ę ending is a common 1st person singular ending:

mam / robię / widzę / czuję / chcę

In pronunciation, final -ę is often only lightly nasal and may sound close to plain -e, especially in fast speech, but it still affects the sound a bit.

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

Po prostu means simply / just (in the sense of nothing more, nothing special).

In your sentence:

chcę po prostu odpocząć ≈ I just want to rest.

Position is quite flexible, and all these are acceptable:

Po prostu chcę odpocząć. – I just want to rest. (stronger emphasis on just)
Chcę po prostu odpocząć. – neutral, common word order
Chcę odpocząć po prostu. – also possible, sounds a bit more colloquial/emphatic at the end

Small shifts in position mostly affect emphasis, not the basic meaning.

Why is it odpocząć and not odpoczywać?

Polish verbs have aspect:

imperfective: ongoing, repeated, or general actions
perfective: single, completed events or goals

Here:

odpoczywać – imperfective: to rest (in progress / as a general activity)
odpocząć – perfective: to rest (have a rest, achieve a state of having rested)

With chcę (I want), we usually choose:

perfective when we mean I want to (successfully) do X (once):
- Chcę odpocząć. – I want to (have a) rest now / at some point.
imperfective when we mean something more general or repeated:
- Lubię odpoczywać. – I like resting (in general).
- Wieczorami lubię odpoczywać. – In the evenings I like to rest / relax.

So chcę odpocząć focuses on one concrete act of resting that you want to accomplish.

Can I change the word order, for example: Wieczorem chcę po prostu odpocząć i czuję zmęczenie?

Polish word order is quite flexible, but not all orders sound equally natural.

Your original:

Wieczorem czuję zmęczenie i chcę po prostu odpocząć.
Logical sequence: In the evening I feel tired, and I (therefore) just want to rest.

If you say:

Wieczorem chcę po prostu odpocząć i czuję zmęczenie.

this is grammatically correct, but it sounds like:

In the evening I just want to rest, and I feel tired (as an additional piece of information).

The natural cause-and-effect feeling (tired → want to rest) is weaker or reversed.
Polish speakers would usually keep something close to the original order to reflect the logical sequence:

Wieczorem czuję zmęczenie i po prostu chcę odpocząć.
Wieczorem czuję zmęczenie, więc chcę po prostu odpocząć. (…so I just want to rest.)

How do you pronounce the nasal vowels ę and ą in words like zmęczenie and odpocząć?

General rules:

ę
- Before a consonant: nasal e, somewhat like French in or en, but fronted:
  - zmęczenie → [zmɛn-CHE-ɲe] (approx.) – nasal quality on mę.
- At the end of a word, it is often only lightly nasal and can sound close to e.
ą
- Before a consonant: nasal o, somewhat like French on:
  - odpocząć → [od-PO-chɔ̃tɕ] – nasal vowel in czą, plus palatalized ć.
- At the end of a word, also often lighter than in careful school pronunciation.

You don’t need to imitate the nasal quality perfectly at first; Polish people will still understand if your ę / ą are not fully nasal, as long as consonants and stress are clear.

Where does the stress fall in Wieczorem czuję zmęczenie i chcę po prostu odpocząć?

Polish almost always has stress on the second-to-last (penultimate) syllable of a word.

Breaking it down:

wie‑CZO‑rem
CZU‑ję
zmę‑CZE‑nie
CHCĘ (one syllable)
po PRO‑stu
od‑PO‑cząć

So you get: wie‑CZO‑rem CZU‑ję zmę‑CZE‑nie i CHCĘ po PRO‑stu od‑PO‑cząć.

Keeping this regular penultimate stress pattern will already make your Polish sound much more natural.