Learn Hardcore Greek: Αυτή η σειρά είναι πολύ ενδιαφέρουσα και δεν είναι βαρετή. - This series is very interesting and is not boring.

So Αυτή points to which series (this one), and η functions as the. Together they make the phrase feel specific and natural, like saying this particular show in English.

What gender is σειρά, and how do I know?

σειρά is a feminine noun.

You can tell from:

Its article: η σειρά (feminine article η).
The adjectives agreeing with it: ενδιαφέρουσα, βαρετή are in the feminine form.

Rough pattern (not a strict rule, but often true): many nouns ending in -α or -η are feminine, especially when they use the article η.

Why is it Αυτή η σειρά and not Αυτή σειρά?

In Greek, when you use a demonstrative (αυτός / αυτή / αυτό = this, εκείνος / εκείνη / εκείνο = that) directly before a noun, you normally also keep the definite article:

Αυτή η σειρά = this series
Αυτό το αυτοκίνητο = this car
Εκείνη η πόλη = that city

Saying Αυτή σειρά is not standard; it sounds incomplete or foreign. The pattern is:

[demonstrative] + [article] + [noun]

Why is Αυτή and not Αυτό or Αυτός used here?

Because σειρά is feminine, the demonstrative must also be feminine in the nominative singular:

Masculine: αυτός ο φίλος (this male friend)
Feminine: αυτή η φίλη (this female friend)
Neuter: αυτό το βιβλίο (this book)

Since σειρά is feminine:

Αυτή η σειρά = this series / show

Why does the verb είναι appear twice? Could I leave one out?

The sentence has two clauses:

Αυτή η σειρά είναι πολύ ενδιαφέρουσα
(και) δεν είναι βαρετή

Each clause has its own verb είναι (is). In Greek, it is very natural to repeat είναι in this kind of contrast:

Είναι καλό και είναι φθηνό. = It is good and (it) is cheap.

You can avoid repeating είναι by changing the structure:

Αυτή η σειρά είναι πολύ ενδιαφέρουσα και όχι βαρετή.
(This series is very interesting and not boring.)

But with δεν, you normally repeat the verb: και δεν είναι βαρετή.

What exactly does πολύ do here, and why isn’t it πολλή?

In πολύ ενδιαφέρουσα, πολύ is an adverb meaning very:

πολύ ενδιαφέρουσα = very interesting

As an adverb, πολύ is invariable (it does not change for gender, number, or case).

There is also πολύς / πολλή / πολύ as an adjective meaning many/much:

πολλή δουλειά = a lot of work (feminine)
πολύ νερό = much water (neuter)

In your sentence, we are modifying an adjective (ενδιαφέρουσα) in the sense of very, so we use the adverb form πολύ.

Why is ενδιαφέρουσα and not ενδιαφέρον used here?

Both come from the same base adjective ενδιαφέρων, -ουσα, -ον meaning interesting, but they must agree with the noun:

Masculine: ενδιαφέρων
Feminine: ενδιαφέρουσα
Neuter: ενδιαφέρον

Since σειρά is feminine:

ενδιαφέρουσα σειρά = interesting series

ενδιαφέρον would be used with a neuter noun:

ενδιαφέρον θέμα = interesting topic

What does δεν do, and where does it go in the sentence?

δεν is the standard negation word for verbs in Greek, like not in English.

Its position is right before the verb:

είναι = (it) is
δεν είναι = (it) is not

Always:

[subject] + (other words) + δεν + [verb] + (rest)

In your sentence:

Αυτή η σειρά / δεν / είναι / βαρετή.
This series / not / is / boring.

What is the difference between δε and δεν?

In speech and informal writing, Greeks often shorten δεν to δε, especially before consonants:

δεν είναι → often pronounced δε(ν) είναι
δεν θέλω → δε θέλω

Spelling rule (neutral recommendation):

In standard written Greek, use δεν.
In very informal texts (messages, chats), you may sometimes see δε, especially before a consonant, but δεν is always safe and correct.

How do ενδιαφέρουσα and βαρετή change if I talk about plural series?

For plural series (σειρές, still feminine), the adjectives must be feminine plural:

Singular:
- Αυτή η σειρά είναι πολύ ενδιαφέρουσα και δεν είναι βαρετή.
Plural:
- Αυτές οι σειρές είναι πολύ ενδιαφέρουσες και δεν είναι βαρετές.

Changes:

Αυτή → Αυτές (feminine plural)
η → οι (feminine plural article)
σειρά → σειρές (plural noun)
ενδιαφέρουσα → ενδιαφέρουσες (feminine plural adjective)
βαρετή → βαρετές (feminine plural adjective)

Could I say Η σειρά αυτή είναι πολύ ενδιαφέρουσα instead of Αυτή η σειρά είναι πολύ ενδιαφέρουσα?

Yes. Both are correct and mean This series/show is very interesting:

Αυτή η σειρά είναι πολύ ενδιαφέρουσα.
Η σειρά αυτή είναι πολύ ενδιαφέρουσα.

Placing the demonstrative:

Before the article: Αυτή η σειρά
After the noun: η σειρά αυτή

Both are used in modern Greek. Many learners find Αυτή η σειρά more straightforward at first.

What is the difference between σειρά meaning series/show and σειρά meaning queue/turn?

Same word, different meanings depending on context:

TV show / series
- Μου αρέσει αυτή η σειρά. = I like this series/show.
Order / sequence
- Με ποια σειρά να τα κάνω; = In what order should I do them?
Queue / one’s turn
- Ποιος είναι ο επόμενος στη σειρά; = Who is next in line?

The sentence you gave is clearly about a TV show/series from the context πολύ ενδιαφέρουσα και δεν είναι βαρετή.

How is ενδιαφέρουσα pronounced, and where is the stress?

ενδιαφέρουσα is stressed on the -φέρ- syllable:

Syllables: εν – δια – φέ – ρου – σα
Approximate pronunciation: en-dia-FE-rou-sa
(more precisely: [enðiaˈferusa])

Pay attention:

The stress mark (´) on έ shows you where to stress: ενδιαφέρουσα.
The ου is one sound like oo in food.