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Using が would mark old movies more as the grammatical subject and often sounds like you’re presenting new information or contrasting with something else. In this simple, general statement, は is the natural choice because you’re talking about old movies in general.

Very roughly:

AはBです → talking about A in general (topic)
AがBです → focusing on A as the subject, often in contrast or as new information

What does 昔 mean exactly? Is it an adjective like old?

昔 is a noun, not an adjective. It means the old days, long ago, in the past.

On its own, it’s like saying long ago or back in the day:

昔、ここに住んでいました。 = Long ago, I lived here.

When you add の and put it before another noun, it works like of the old days:

昔の映画 = movies of the old days → old movies / movies from long ago

Could we say 古い映画は短いです instead of 昔の映画は短いです? What’s the difference?

You can say 古い映画は短いです, but the nuance is slightly different.

昔の映画: movies that were made in the past; movies from long ago (focus on time period).
古い映画: movies that are old as objects or in age; also can feel like old-fashioned (focus on age/oldness itself).

Often they overlap, but:

If you want to emphasize period (e.g., movies from the 1950s), 昔の映画 feels more natural.
If you just mean this movie is old (not new), 古い映画 is more neutral.

Why is it 短いです and not just 短い?

短い is an い-adjective meaning short.
To make a polite sentence, you can use:

短いです → polite
短い (by itself) → plain / casual, often used in neutral statements or in dictionaries.

So:

昔の映画は短いです。 → polite speech
昔の映画は短い。 → casual speech, used with friends, in writing, etc.

Both are grammatically correct; the difference is politeness level.

Is です necessary with an い-adjective like 短い?

Grammatically, です is not necessary. The sentence is complete with just the い-adjective:

昔の映画は短い。 → This is a full, correct sentence.

Adding です does two things:

Makes the sentence politer.
Softens the tone a bit (less blunt).

In everyday polite conversation, 短いです is very common. In informal conversation or in written explanations, you will often see just 短い.

How would I say “Old movies were short” (past tense), not “are short”?

To make an い-adjective past tense, you change い to かった:

短い → 短かった (was short)

Then, for polite speech, add です (or です becomes でした after nouns/な-adjectives, but with い-adjectives です stays after the conjugated form):

昔の映画は短かったです。
= Old movies were short.

Plain (casual) past:

昔の映画は短かった。

Does 昔の映画 mean one old movie or old movies? Where is the plural?

Japanese usually does not mark plural the way English does.
昔の映画 can mean:

an old movie
old movies

Which one it is depends on context.
In 昔の映画は短いです。 it’s clearly a general statement, so we understand it as old movies (in general).

Why are there spaces between words in 昔　の　映画　は　短い　です。? I thought Japanese doesn’t use spaces.

You’re right: normal Japanese writing does not use spaces between words.
The version with spaces is usually for teaching purposes, to show you where each word or particle is:

昔｜の｜映画｜は｜短い｜です。

In real Japanese text, you would write it as:

昔の映画は短いです。

Can I change the word order, like 映画の昔は短いです?

No, that word order is not natural. In Japanese:

Modifiers come before the noun they modify.
- 昔の映画 (昔の modifies 映画)
The topic (marked by は) generally comes near the beginning.

So 昔の映画は短いです。 is the natural order.
映画の昔は短いです would be interpreted as something like the old days of movies are short, which doesn’t make sense.

Where is the subject they in Old movies are short? Why isn’t it in the Japanese sentence?

Japanese often omits the subject when it’s clear from context.

In 昔の映画は短いです。 the topic 昔の映画 already tells us what we’re talking about, so there’s no need for they or they are. The are is built into the structure 短いです.

So:

English: Old movies are short.
Japanese: 昔の映画は短いです。
(literally: As for old movies, [they] are short.)

The [they] is understood but not spoken.