На первом слайде была только фотография, а на втором — понятная диаграмма.

Because на is being used to mean on a slide, so it takes the prepositional case for location.

• слайд → на слайде
• первый → на первом
• второй → на втором

So:

• на первом слайде = on the first slide
• на втором = on the second one

In the second part, слайде is omitted because it is understood from context.

The verb agrees with the noun that is really the subject of the clause: фотография.

• фотография is feminine singular
• so the past tense of быть must also be feminine singular: была

Even though фотография comes after the verb, it still controls agreement:

• На первом слайде была только фотография.

If the noun were masculine, you would get был. If it were neuter, было. If plural, были.

Russian often leaves out a repeated verb when it is easy to understand from context.

So this:

• а на втором — понятная диаграмма

really means:

• а на втором была понятная диаграмма

The dash shows that something has been omitted, especially a repeated verb such as была. This is very natural in Russian.

The dash marks an ellipsis: a missing word or words that the reader can easily supply.

Here it replaces the repeated verb:

• На первом слайде была только фотография, а на втором — понятная диаграмма.

The full version would be:

• На первом слайде была только фотография, а на втором была понятная диаграмма.

Russian often uses this kind of dash in comparisons or contrasts to avoid repetition.

А is very common when Russian contrasts two things side by side.

Here the sentence is comparing two slides:

• on the first slide: only a photo
• on the second slide: a clear diagram

So а works like whereas, while, or sometimes a mild but.

• и would simply add information: and
• но would sound more like a stronger contradiction: but

In this sentence, а is the most natural choice because it sets up a contrast rather than a dramatic opposition.

Because they are the main nouns of their clauses: the things that were on the slides.

Russian often uses the nominative in sentences of the type:

• На столе была книга. = There was a book on the table.

So here:

• была фотография
• была диаграмма

Both nouns are nominative because they are the items being identified as present.

Because понятная диаграмма is a nominative noun phrase, not an instrumental one.

• диаграмма is feminine singular nominative
• the adjective must agree with it:
  • понятная

So:

• понятная диаграмма = a clear / understandable diagram

If you used понятной диаграммой, that would be instrumental, which does not fit this sentence.

Только means only.

In this sentence, it most naturally modifies фотография:

• была только фотография = there was only a photograph

The idea is that the first slide contained nothing else of importance besides the photograph.

Word position matters. Putting только near the word it modifies is normal Russian style.

Yes, Russian word order is quite flexible, but different orders change the emphasis.

The given version:

• На первом слайде была только фотография...

is natural because it starts with the location, then says what was there.

Other possible orders:

• Только фотография была на первом слайде.
• Фотография была только на первом слайде.

These do not all mean exactly the same thing in emphasis:

• На первом слайде была только фотография focuses on the content of the first slide.
• Только фотография была на первом слайде emphasizes that it was only a photograph.
• Фотография была только на первом слайде can mean the photograph was only on the first slide, not elsewhere.

So yes, the order can change, but the nuance changes too.

Because Russian often omits a repeated noun when it is obvious.

The full phrase would be:

• на втором слайде

But after на первом слайде, Russian can shorten the second phrase to:

• на втором

This is very natural and efficient. English does something similar:

• on the first slide ..., and on the second ...

They are ordinal numerals, but in Russian they behave grammatically like adjectives.

That means they:

• change for case
• change for gender
• change for number
• agree with the noun they describe

So:

• первый слайд = nominative masculine singular
• на первом слайде = prepositional masculine singular

And similarly:

• второй слайд
• на втором слайде

This is why their endings change just like normal adjectives.