Rivelinte la foton, ŝi kontrolas la kontraston.

Rivelinte is an adverbial active past participle.

It is formed like this:

• rivel- = the verb root
• -int- = active participle for an action completed earlier
• -e = adverb ending

So rivelinte means something like having revealed / having developed.

In this sentence, it shows that this action happened before the main verb:

• Rivelinte la foton, ŝi kontrolas la kontraston.
• Having developed the photo, she checks the contrast.

Because it is being used adverbially, not adjectivally.

• -a participles describe a noun: rivelinta virino = a woman who has revealed/developed
• -e participles describe the action of the clause: rivelinte = having revealed/developed

Here, rivelinte la foton does not directly describe ŝi as an adjective would. Instead, it gives the circumstance of the main action: after doing X, she does Y.

The subject is understood to be the same as the subject of the main clause: ŝi.

So the sentence means:

• She developed the photo
• then she checks the contrast

This is a normal feature of Esperanto adverbial participles. The implied subject of rivelinte is normally the same as the subject of the main verb unless something else makes it very clear.

They both have -n because they are direct objects.

• la foton = the thing that was developed
• la kontraston = the thing that she checks

In Esperanto, direct objects usually take -n.

Compare:

• ŝi kontrolas la kontraston = she checks the contrast
• ŝi promenas = she walks
  no direct object, so no -n

Because the sentence is presented in the present tense: she checks.

The participle rivelinte only tells you that the developing happened before the checking. It does not force the whole sentence into the past tense.

So this structure means:

• first: developing the photo
• then: checking the contrast

If you wanted the whole sentence in the past, you could say:

• Rivelinte la foton, ŝi kontrolis la kontraston.

That would mean Having developed the photo, she checked the contrast.

More or less, yes.

These are close in meaning:

• Rivelinte la foton, ŝi kontrolas la kontraston.
• Post kiam ŝi rivelis la foton, ŝi kontrolas la kontraston.

The participial version is just more compact.

A very literal sense is:

• Having developed the photo, she checks the contrast.

A more natural English translation might be:

• After developing the photo, she checks the contrast.

-int- shows that the action is already completed relative to another action.

Here is the contrast:

• rivelante = while developing
• rivelinte = having developed
• rivelonte = about to develop / going to develop

So in your sentence:

• Rivelinte la foton... means the photo has already been developed before she checks the contrast.

Yes. Esperanto word order is fairly flexible because endings show the grammar.

You could also say:

• Ŝi kontrolas la kontraston, rivelinte la foton.

But the original order is very natural because it presents the earlier action first:

1. develop the photo
2. check the contrast

So the original version sounds smooth and clear.

La is the definite article, meaning the.

So:

• la foton = the photo
• la kontraston = the contrast

This suggests a specific photo and a specific contrast, probably the contrast of that photo in the situation being described.

Esperanto has only one definite article, la, and it does not change for gender, number, or case.

Only that ŝi means she and is the subject of kontrolas.

Esperanto personal pronouns do not change form the way English subject/object pronouns do as much, except when -n is added for the accusative:

• ŝi = she
• ŝin = her

In this sentence, ŝi is the doer of the action, so no -n is used.

Yes. In fact, for natural English, that is often the best choice.

Although rivelinte literally matches having developed, English often prefers:

• After developing the photo, she checks the contrast.

So both ideas are useful:

• literal grammar sense: having developed
• natural English sense: after developing