Коллега попросила вставить эту диаграмму на последний слайд и не забыть про подпись.

Because коллега is a common-gender noun in Russian. It can refer to either a male or a female colleague.

In the past tense, the verb agrees with the actual person’s gender:

• коллега попросил = the colleague (male) asked
• коллега попросила = the colleague (female) asked

So here, попросила tells you the colleague is female.

Some Russian nouns ending in -а / -я can refer to either men or women. Коллега is one of them.

That means:

• the noun form stays the same: коллега
• but adjectives and past-tense verbs show the real gender of the person

For example:

• мой коллега попросил = my male colleague asked
• моя коллега попросила = my female colleague asked

So the ending of the noun itself does not always tell you the person’s sex.

This is a very common Russian pattern:

• попросить + infinitive

It means to ask someone to do something.

So:

• попросила вставить = asked someone to insert
• попросила не забыть = asked someone not to forget

Russian often leaves out the person being asked if it is obvious from context. In English, we usually need something like asked me, asked us, or asked him. In Russian, that object can be omitted.

A fuller version could be:

• Коллега попросила меня вставить эту диаграмму...
• My colleague asked me to insert this diagram...

But in your sentence, меня is simply left unstated.

Вставить is the perfective form, and вставлять is the imperfective form.

Here, the colleague is asking for a single completed action:

• put the diagram into the slide
• finish that task

So Russian uses the perfective вставить.

Compare:

• вставить = to insert once, successfully, as a completed action
• вставлять = to be inserting, to insert repeatedly, or in a general/process sense

After попросить, Russian very often uses a perfective infinitive when the request is about a one-time result.

The same idea appears in не забыть:

• забыть is also perfective
• it means not to forget in the sense of making sure that the forgetting does not happen

Because диаграмма is the direct object of вставить, so it goes into the accusative case.

Диаграмма is feminine singular, so:

• nominative: эта диаграмма
• accusative: эту диаграмму

Both words change:

• эта → эту
• диаграмма → диаграмму

This is a very common feminine accusative pattern in Russian.

Because на can take different cases depending on the meaning.

Here the idea is direction / placement onto the slide, so Russian uses the accusative:

• на последний слайд = onto the last slide

If you were talking about location, Russian would use the prepositional:

• на последнем слайде = on the last slide

So compare:

• вставить на последний слайд = insert onto the last slide
• быть на последнем слайде = be on the last slide

This is an important motion-vs-location distinction in Russian.

Because after на in this sentence, the noun is in the accusative case, not the prepositional.

Слайд is a masculine inanimate noun, and for masculine inanimate nouns, the accusative singular is the same as the nominative:

• nominative: последний слайд
• accusative: последний слайд

So the form stays the same.

If it were location, you would get:

• на последнем слайде

There, both the adjective and noun change because the case is different.

Russian often links two requested actions very directly:

• попросила вставить ... и не забыть ...

This means the colleague asked someone:

1. to insert the diagram
2. and not to forget the caption

It is compact and natural in Russian.

A version with чтобы is possible in other sentence structures, but here попросить + infinitive is the simplest and most standard pattern.

So the two infinitives вставить and не забыть both depend on попросила.

Не забыть про подпись means not to forget about the caption/signature/label.

The preposition про adds the sense of about or as for. In this sentence, it sounds like a reminder:

• don’t forget about the caption

If you said не забыть подпись, that would sound less natural here and could suggest forgetting the caption itself as an object, rather than forgetting to include it.

So:

• не забыть про подпись = don’t forget about the caption / remember to include it

This is very common colloquial Russian.

After про, Russian uses the accusative case.

Here that gives:

• про подпись

For this noun, the accusative singular has the same form as the nominative because подпись is an inanimate feminine noun of the soft-sign type.

So:

• nominative: подпись
• accusative: подпись

The form looks unchanged, but the case is still accusative because of про.

In general, подпись can mean:

• signature
• caption
• label

In this sentence, because we are talking about a diagram on a slide, the most likely meaning is:

• caption
• or possibly label / caption text

It almost certainly does not mean a handwritten signature here.

So не забыть про подпись is basically saying:

• don’t forget the caption/label for the diagram

The person being asked — the understood object of попросила.

So the structure is basically:

• A colleague asked [someone] to insert this diagram... and not to forget the caption.

Russian does not need to repeat that person before each infinitive. Both infinitives depend on попросила and refer to the same understood person.

No, Russian word order is fairly flexible, though this version is natural and neutral.

This sentence:

• Коллега попросила вставить эту диаграмму на последний слайд и не забыть про подпись.

sounds like a normal, straightforward statement.

Russian could rearrange parts for emphasis, for example:

• Коллега попросила на последний слайд вставить эту диаграмму...
• Эту диаграмму коллега попросила вставить на последний слайд...

These versions shift emphasis a bit, but the basic meaning stays the same.

So the given word order is natural, but not the only possible one.