Η πρώτη μου εντύπωση ήταν ότι νοιάζεται πραγματικά για τους άλλους.

Because εντύπωση is a feminine noun, and the adjective πρώτη (first) has to agree with it in gender, number, and case.

• η εντύπωση = the impression (feminine singular)
• η πρώτη εντύπωση = the first impression

So:

• ο πρώτος would be masculine
• το πρώτο would be neuter
• η πρώτη is the correct feminine form here

In Greek, short possessive words like μου (my), σου (your), του/της (his/her) often come after the noun phrase.

So:

• η πρώτη μου εντύπωση = my first impression

This is very natural Greek word order.
You can think of it as:

• η πρώτη εντύπωση μου

but in standard modern Greek, the usual form is:

• η πρώτη μου εντύπωση

The little word μου is an unstressed clitic, so it usually sits in a fixed position rather than behaving like a full adjective such as my in English.

It is in the nominative, because it is the subject of the sentence.

The structure is:

• Η πρώτη μου εντύπωση = subject
• ήταν = was
• ότι... = that...

So the sentence literally starts with My first impression was...

Ήταν is the past tense of είμαι (to be). It means was.

So:

• είναι = is
• ήταν = was

Since the sentence talks about a past impression, Greek uses ήταν:

• Η πρώτη μου εντύπωση ήταν...
• My first impression was...

Ότι means that and introduces a content clause, just like English that in:

• My impression was that...

So:

• Η πρώτη μου εντύπωση ήταν ότι...
• My first impression was that...

In everyday Greek, πως can often be used in a similar way:

• Η πρώτη μου εντύπωση ήταν πως...

But ότι is perfectly standard and very common.

Νοιάζεται comes from the verb νοιάζομαι, which means:

• to care
• to be concerned
• to take an interest

In this sentence:

• νοιάζεται για τους άλλους = he/she cares about others

A useful thing to know is that νοιάζομαι looks like a passive-form verb, but its meaning here is active. This is common in Greek: some verbs have middle/passive endings but active meanings.

Because the verb here is νοιάζομαι, not νοιάζω.

Its present-tense forms are like:

• νοιάζομαι = I care
• νοιάζεσαι = you care
• νοιάζεται = he/she cares
• νοιαζόμαστε = we care
• νοιάζεστε = you all care
• νοιάζονται = they care

So νοιάζεται is the correct third person singular form: he/she cares.

This is very natural in Greek. The main verb is in the past:

• Η πρώτη μου εντύπωση ήταν... = My first impression was...

But the content of that impression can still be expressed in the present if it describes a general or ongoing quality:

• ότι νοιάζεται πραγματικά για τους άλλους
• that he/she really cares about others

English often does the same:

• My first impression was that he really cares about others.

Greek does not need to shift the tense backward just because the main verb is past.

Greek often leaves out subject pronouns because the verb ending already shows the person and number.

• νοιάζεται = he/she cares

So the subject pronoun is understood from context. Greek is a pro-drop language.

If you wanted to add the pronoun for emphasis, you could say:

• ότι αυτός νοιάζεται... = that he cares...
• ότι αυτή νοιάζεται... = that she cares...

But normally, Greek does not include it unless there is some reason to stress it.

Πραγματικά is an adverb meaning:

• really
• truly
• genuinely

It modifies νοιάζεται:

• νοιάζεται πραγματικά = really cares

It adds the idea that the caring is sincere, not superficial.

Because νοιάζομαι για means to care about.

So the pattern is:

• νοιάζομαι για κάποιον / κάτι
• care about someone / something

Examples:

• Νοιάζομαι για σένα. = I care about you.
• Νοιάζεται για την οικογένειά του. = He/She cares about his/her family.

Since για takes the accusative, we get:

• τους άλλους = accusative plural

Because after the preposition για, Greek uses the accusative case.

Compare:

• οι άλλοι = the others (nominative, subject form)
• τους άλλους = the others (accusative, object form)

Since για requires the accusative, τους άλλους is correct.

Not necessarily. Grammatically, άλλους is masculine plural accusative, but in Greek, the masculine plural is often used for:

• a mixed group of people
• people in general

So για τους άλλους usually means:

• about others
• about other people

If the speaker specifically meant only women, they would say:

• για τις άλλες

But in a general statement like this, τους άλλους is the normal choice.

The word order is very natural and neutral.

• Η πρώτη μου εντύπωση = topic/subject
• ήταν = linking verb
• ότι νοιάζεται πραγματικά για τους άλλους = what the impression was

Greek word order is often more flexible than English, but this sentence follows a very straightforward pattern.
The adverb πραγματικά sits before the prepositional phrase:

• νοιάζεται πραγματικά για τους άλλους

That is the most natural placement here.

A rough pronunciation guide is:

• ee PROH-tee moo eh-DEEP-oh-see EE-tan OH-tee NYAH-zeh-te prag-ma-ti-KA ya toos AL-loos

A few helpful points:

• η sounds like ee
• ντ would sound like d, but there is no ντ here
• οι / η / ι / υ / ει usually sound like ee
• για sounds roughly like ya
• νοιάζεται has the stress on -ά-
• πραγματικά has the stress on the last syllable: -κά

Yes. That is also correct and very natural.

You can say:

• Η πρώτη μου εντύπωση ήταν ότι...
• Η πρώτη εντύπωσή μου ήταν ότι...

Both mean the same thing: My first impression was that...

The second version attaches the possessive more closely to the noun. Both are common, and the difference is mostly one of style and rhythm rather than meaning.