Learn Hardcore Russian: Этот подкаст короткий, но очень полезный.

English: This podcast is short but very useful.
Russian: Этот подкаст короткий, но очень полезный.
(literally: This podcast short, but very useful.)

You only explicitly use forms of быть in:

the past: Этот подкаст был коротким... (was short…)
the future: Этот подкаст будет коротким... (will be short…)
or for special emphatic/very formal uses in the present, which are rare in everyday speech.

Why is it Этот, not Эта, Это, or Эти?

Этот is the masculine singular form of “this” and must agree with the noun подкаст in gender and number.

The forms of “this” in the nominative are:

Этот – masculine singular (for он nouns)
Эта – feminine singular (for она nouns)
Это – neuter singular (for оно nouns)
Эти – plural (for они nouns, any gender)

Since подкаст is treated as masculine singular, you use Этот подкаст = this podcast.

Why are короткий and полезный in this form? What are these endings?

Both короткий and полезный are adjectives in masculine singular nominative, agreeing with подкаст.

короткий: stem коротк-
- ending -ий (spelled -кий as a common pattern)
полезный: stem полезн-
- ending -ый (spelled -ный, also a common pattern)

For a masculine singular noun like подкаст, the basic descriptive form of an adjective in the nominative is typically:

-ый / -ий / -ой (spelling and phonetic rules decide which one)

So:

Этот подкаст короткий. – This podcast is short.
Этот подкаст полезный. – This podcast is useful.

Both adjectives match the noun in:

gender: masculine
number: singular
case: nominative

What case are the words in, and why?

All three content words here are in the nominative case:

Этот подкаст – nominative (subject)
короткий – nominative (predicate adjective)
полезный – nominative (predicate adjective)

In equational sentences like “X is Y” with adjectives, Russian uses the nominative for both the subject and the adjective:

Подкаст короткий. – The podcast is short.
Фильм интересный. – The film is interesting.

Unlike some languages, Russian does not switch the adjective to a different case here; it stays nominative.

Why is there a comma before но?

Но means “but” and it introduces a contrast. In Russian, when you join two parts of a sentence with но, you normally put a comma before it:

Он устал, но доволен. – He is tired, but satisfied.
Подкаст короткий, но полезный. – The podcast is short, but useful.

In your example, the two parts being contrasted are:

короткий (short)
очень полезный (very useful)

So the comma before но is standard punctuation.

Could I use а instead of но here? What is the difference?

You could say:

Этот подкаст короткий, а очень полезный.

but it would sound a bit off or incomplete to most native speakers; usually you’d repeat the noun or pronoun with а in this kind of contrast:

Этот подкаст короткий, а другой — длинный.
This podcast is short, whereas another one is long.

General nuance:

но = “but” with a clearer sense of opposition or “despite that”.
→ It’s short, but (despite that) very useful.
а = often “whereas / while / and” with a milder contrast or comparison.
→ This one is X, whereas that one is Y.

In your sentence, но is the natural choice, because it emphasizes the unexpected positive side (very useful) despite the negative/neutral side (short).

Can I change the word order, like Этот подкаст очень полезный, но короткий? Does it change the meaning?

Yes, this order is also grammatically correct:

Этот подкаст очень полезный, но короткий.

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

Этот подкаст короткий, но очень полезный.
→ First focuses on “short”, then contrasts that with “but very useful”.
→ Feels like: It may be short, but the important point is that it’s very useful.
Этот подкаст очень полезный, но короткий.
→ First highlights “very useful”, then adds “but (unfortunately) short”.
→ Feels like: It’s very useful, but the drawback is that it’s short.

Russian word order is flexible, and here the change is about information flow and emphasis, not grammar.

Why not say Этот короткий подкаст очень полезный? How is that different?

Этот короткий подкаст очень полезный. is also correct but has a slightly different structure and feel.

Этот подкаст короткий
→ короткий is a predicate: This podcast is short.
Этот короткий подкаст
→ короткий is an attributive adjective modifying podcast: this short podcast.

So:

Этот подкаст короткий, но очень полезный.
→ Describes the podcast using two separate qualities in a contrast: short, but very useful.
Этот короткий подкаст очень полезный.
→ Treats short podcast as one noun phrase (this short podcast), then adds that it is very useful. There is no explicit contrast like “but”.

The original sentence highlights a contrast between “short” and “very useful.”
The alternative makes “short podcast” sound more like a neutral description, without the “but” idea.

What exactly does очень do here? Can I move it or leave it out?

Очень means “very”, and it intensifies полезный (useful):

полезный – useful
очень полезный – very useful

About position and omission:

Normal position: очень полезный
→ Очень (adverb) goes directly before the adjective it modifies.
You can omit it:
Этот подкаст короткий, но полезный.
→ Meaning: short but useful (less strong than “very useful”).
Putting it at the end: …но полезный очень
→ This is possible but sounds colloquial or poetic and with special emphasis. In neutral speech, you’d keep очень before the adjective.

So, the neutral and most natural version is exactly what you have: очень полезный.

Why is подкаст masculine? How do I know the gender of such foreign words?

Most recent loanwords for inanimate objects in Russian are automatically treated as masculine by default, especially when they end in a consonant:

подкаст, фильм, сайт, чарт, клип – masculine
They take он (he/it) as a pronoun and use masculine adjective forms:
интересный подкаст, новый сайт, etc.

There are some borrowed words that are neuter (кафе, метро) or feminine (пицца), but with a word like подкаст ending in a consonant, the safe assumption is masculine.

Could we say Этот подкаст полезен instead of полезный? What’s the difference?

Yes:

Этот подкаст полезен. – correct
Этот подкаст полезный. – also correct

Полезен is a short-form adjective, while полезный is a full-form adjective.

General tendencies:

Full form (полезный) is the default in modern spoken Russian, used for ordinary descriptions:
Фильм интересный. Курс полезный.
Short form (полезен) often sounds:
- a bit more formal, bookish, or categorical
- common in written language, official style, or set phrases
  Example: Этот совет действительно полезен.

In your specific sentence:

Этот подкаст короткий, но очень полезный. – natural, conversational.
Этот подкаст короткий, но очень полезен. – also correct, but a little more formal/“statement-like”.

Both mean essentially the same thing.