Устный доклад был коротким.

Because it is part of the predicate after был (was).

In Russian, when a noun or a full adjective comes after быть in the past or future tense, it is very often put in the instrumental case:

• Доклад был коротким. = The presentation/report was short.
• Он был учителем. = He was a teacher.

So here:

• короткий = nominative masculine singular
• коротким = instrumental masculine/neuter singular

Using the instrumental here is the standard, natural choice.

You may sometimes see nominative in similar sentences, but был коротким is the normal form learners should use.

Because был agrees with the subject, which is доклад.

Доклад is:

• masculine
• singular

So the past tense form of быть is:

• был for masculine singular
• была for feminine singular
• было for neuter singular
• были for plural

Compare:

• Доклад был коротким. = The report was short.
• Лекция была короткой. = The lecture was short.
• Выступление было коротким. = The speech was short.
• Доклады были короткими. = The reports were short.

It is in the nominative case, because it is the subject of the sentence.

• устный modifies доклад
• both are masculine singular nominative

So:

• устный = oral, spoken
• доклад = report, presentation, talk

Together, устный доклад means an oral report / oral presentation.

Доклад usually means a report, presentation, or formal talk.

Depending on context, English translations might include:

• report
• presentation
• talk
• address

It often sounds a bit more formal than casual English talk. In a school, university, conference, or official setting, доклад is a very common word.

So устный доклад is something like:

• an oral report
• an oral presentation

In Russian, the verb быть (to be) is normally omitted in the present tense.

So:

• Устный доклад короткий. = The oral presentation is short.

But in the past tense, Russian does use a form of быть:

• Устный доклад был коротким. = The oral presentation was short.

And in the future:

• Устный доклад будет коротким. = The oral presentation will be short.

So the missing present-tense is is completely normal in Russian.

Yes. That uses the short form adjective короток instead of the full form коротким.

Both mean roughly the same thing:

• Устный доклад был коротким.
• Устный доклад был короток.

But there is a style difference:

• был коротким is the more everyday, neutral pattern
• был короток can sound more literary, formal, or stylistically marked

For learners, был коротким is the safer and more generally useful version.

Yes. Russian word order is fairly flexible, though the neutral order here is perfectly natural:

• Устный доклад был коротким.

You could also say:

• Доклад был коротким.
  If oral is not important or already understood.

• Коротким был устный доклад.
  Possible, but more marked, often for emphasis.

• Доклад был устным и коротким.
  If you want to state both qualities as new information.

Russian word order often changes emphasis rather than basic meaning.

Because they do different jobs in the sentence.

• устный is part of the subject noun phrase: устный доклад
• коротким is part of the predicate after был

So:

1. устный доклад = the oral presentation
   This is the subject, so it stays in the nominative.

2. был коротким = was short
   This is the predicate, and the adjective after был is commonly instrumental.

That is why the two adjectives have different endings.

The ending -ым marks the instrumental singular form of a hard-stem masculine or neuter adjective.

Base form:

• короткий = short

Instrumental singular:

• коротким

Other examples:

• новый → новым
• интересный → интересным
• русский → русским

So коротким is just the instrumental form of короткий.

Yes, basically. Устный means oral, spoken, or delivered by speech rather than in writing.

Common combinations include:

• устный доклад = oral presentation
• устный экзамен = oral exam
• устный перевод = interpreting / oral translation
• устная речь = spoken speech / oral speech

So here устный доклад clearly means a presentation given aloud, not a written report.

Because Russian has no articles.

So Устный доклад был коротким could mean, depending on context:

• The oral presentation was short
• An oral presentation was short

Russian leaves that distinction to context, word order, and the situation.

This is one of the big differences from English: Russian usually does not explicitly mark the vs a/an.