Learn Hardcore Greek: Στο λιμάνι βλέπω πλοία και πολλά ταξί που περιμένουν τους τουρίστες. - At the port I see ships and many taxis that are waiting for the tourists.

We use το because λιμάνι is a neuter noun (το λιμάνι). After σε, nouns normally go in the accusative case; for neuter, nominative and accusative have the same form (λιμάνι), so the noun does not visibly change.

Why is λιμάνι in this form? What gender and case is it, and how does it decline?

Λιμάνι is:

Gender: neuter
Base form: το λιμάνι (the port)
Case here: accusative singular, required after σε / στο

Declension of το λιμάνι (pattern of many neuter nouns in -ι):

Nominative singular: το λιμάνι (the port – subject)
Genitive singular: του λιμανιού (of the port)
Accusative singular: το λιμάνι (the port – object / after preposition)
Nominative plural: τα λιμάνια (the ports)
Genitive plural: των λιμανιών
Accusative plural: τα λιμάνια

In this sentence, στο λιμάνι uses λιμάνι in the accusative because it follows the preposition σε, which takes the accusative.

Why is there no I before βλέπω? Is it wrong to say Εγώ βλέπω?

Greek usually omits subject pronouns like εγώ because the verb ending already shows the subject.

βλέπω = I see
(1st person singular is clear from the -ω ending)

So:

Βλέπω πλοία = I see ships.

You can say Εγώ βλέπω πλοία, but:

It adds emphasis: I see ships (as opposed to someone else).
In neutral, everyday speech, you simply say Βλέπω… without εγώ.

What is the difference between πλοία and καράβια? Would καράβια work here?

Both refer to ships, but there is a nuance:

πλοίο (plural πλοία) is a bit more formal / neutral, used for ships in general, especially larger or official ones (ferries, cargo ships, naval ships).
καράβι (plural καράβια) is more colloquial and can feel slightly more informal or generic.

In this sentence, you could say:

Στο λιμάνι βλέπω καράβια και πολλά ταξί…

It would still be natural. Πλοία sounds a bit more standard/formal, but everyday speakers do use both.

Why is it πολλά ταξί and not something like πολλά ταξιά? Does ταξί ever change form?

Ταξί is an indeclinable loanword (from French taxi). That means its form does not change for gender, number, or case.

Singular: το ταξί (the taxi)
Plural: τα ταξί (the taxis)
Accusative: still το ταξί / τα ταξί

The adjective πολλά (many) does change and agrees with the noun in gender and number:

Masculine plural: πολλοί (e.g. πολλοί άνθρωποι)
Feminine plural: πολλές (e.g. πολλές γυναίκες)
Neuter plural: πολλά (e.g. πολλά παιδιά, πολλά ταξί)

So we get πολλά ταξί: adjective in neuter plural, noun in its unchanged form.

What does που do in ταξί που περιμένουν τους τουρίστες? Is it like που = where or that?

Here που is a relative pronoun, meaning that / which / who.

πολλά ταξί που περιμένουν τους τουρίστες
= many taxis that are waiting for the tourists

It links ταξί with the clause περιμένουν τους τουρίστες and describes those taxis.

In Modern Greek, που is the most common relative pronoun and is used for people, animals, things, places, etc.:

ο άνθρωπος που είδα (the man who I saw)
το βιβλίο που διαβάζω (the book that I’m reading)
το μέρος που μένω (the place where I live)

More formal alternatives like ο οποίος / η οποία / το οποίο exist, but που is what you hear all the time in speech.

Why is the verb περιμένουν (they wait) in plural? Shouldn’t a neuter plural sometimes take a singular verb in Greek?

The subject of περιμένουν is ταξί (actually πολλά ταξί), which is plural, so the normal Modern Greek rule is:

plural subject → plural verb
πολλά ταξί … περιμένουν (many taxis are waiting)

In older Greek and in some more formal styles, a neuter plural (especially inanimate) can sometimes take a singular verb (a remnant of Ancient Greek), but in Modern spoken Greek:

Τα ταξί περιμένουν is the standard, natural form.
Τα ταξί περιμένει would sound wrong or at best very odd today.

So the plural περιμένουν is exactly what you want here.

Why is it τους τουρίστες and not οι τουρίστες? What case is this, and why do we need the article?

Τους τουρίστες is in the accusative plural, because it is the direct object of the verb περιμένουν (they are waiting for whom?).

Noun: ο τουρίστας (the tourist)
Plural: οι τουρίστες
Accusative plural: τους τουρίστες

Pattern:

Nominative plural (subject): οι τουρίστες (the tourists)
Accusative plural (object): τους τουρίστες (the tourists – object)

We use τους instead of οι because:

οι is nominative plural (subject form)
τους is accusative plural (object form)

The definite article is used because we are talking about specific tourists that are expected at that port (e.g. tourists arriving on certain ships), not just tourists in general.

Without the article:

περιμένουν τουρίστες
= they are waiting for tourists (tourists in general, not specific known ones)

With the article:

περιμένουν τους τουρίστες
= they are waiting for the tourists (previously known / expected group)

Could we change the word order, like Βλέπω στο λιμάνι πλοία και πολλά ταξί? Does it change the meaning?

Yes, you can change the word order. All of these are grammatical:

Στο λιμάνι βλέπω πλοία και πολλά ταξί…
Βλέπω στο λιμάνι πλοία και πολλά ταξί…
Βλέπω πλοία και πολλά ταξί στο λιμάνι…

The basic meaning is the same, but the emphasis shifts slightly:

Στο λιμάνι βλέπω…
Emphasis starts with location: At the port, I see…
Βλέπω στο λιμάνι…
Slightly more neutral; focus is on I see, then where.
Βλέπω πλοία και πολλά ταξί στο λιμάνι
Emphasis first on what you see, then you add where.

Greek word order is flexible; you usually keep related words close for clarity (e.g. στο λιμάνι near βλέπω, and που περιμένουν right after ταξί).

Can we omit the article and say σε λιμάνι βλέπω πλοία… or βλέπω πλοία σε λιμάνι? Would that sound natural?

You can grammatically say σε λιμάνι, but it changes the meaning:

στο λιμάνι = at the port (a specific, known port – the place we have in mind)
σε λιμάνι = at a port (some port, not specified which)

So:

Στο λιμάνι βλέπω πλοία…
I’m talking about a particular port (the one we are at / already know about).
Σε λιμάνι βλέπω πλοία…
Sounds like a more abstract or story-like statement: at some port, I see ships…

In everyday speech, for concrete locations that speaker and listener can identify, the article (στο, στον, στη) is almost always used.