Он работает недостаточно быстро.

Yes, Russian can omit the subject pronoun when it is clear from context.

• Он работает недостаточно быстро. = He works / He is working not fast enough.
• Работает недостаточно быстро. = (He) works / is working not fast enough, if everyone already knows who is being discussed.

Here, он is included because the speaker wants to state the subject explicitly.

Работает is the 3rd person singular present tense form of работать.

The verb changes like this:

• я работаю = I work
• ты работаешь = you work
• он / она работает = he / she works
• мы работаем = we work
• вы работаете = you work
• они работают = they work

Because the subject is он (he), the verb must be работает.

It can mean either one, depending on context.

Russian does not always separate:

• He works
• He is working

with different verb forms the way English often does.

So Он работает недостаточно быстро can mean:

• He works too slowly / not fast enough in general, or
• He is working too slowly / not fast enough right now

The context tells you which meaning is intended.

Because this sentence describes a process or manner of working, not a completed action.

Работать is imperfective, and imperfective is used for:

• ongoing actions
• repeated actions
• general statements
• descriptions of how something is happening

Here the idea is about how he works: not fast enough. That naturally calls for the imperfective verb работает.

Here недостаточно means not enough or insufficiently.

It modifies the adverb быстро:

• быстро = quickly
• недостаточно быстро = not quickly enough

So the phrase literally means something like:

• insufficiently quickly
• more natural English: not fast enough

In this sentence, недостаточно is normally written as one word because it functions as a single adverb meaning insufficiently / not enough.

• Он работает недостаточно быстро. = neutral, standard: He doesn’t work fast enough.

The separate spelling не достаточно is possible in some contexts, but usually when there is stronger contrast or emphasis, for example:

• Он работает не достаточно быстро, а слишком медленно.

For a learner, the safe default for this sentence is недостаточно as one word.

Because быстро is an adverb, and adverbs do not change for:

• gender
• number
• case

It comes from the adjective быстрый (fast, quick), but once it becomes the adverb быстро, it stays the same.

Compare:

• быстрый работник = a fast worker
• работает быстро = works quickly

Yes, Russian word order is flexible.

The neutral order here is:

• Он работает недостаточно быстро.

But you can also say:

• Он недостаточно быстро работает.

Both are grammatical. The difference is mostly emphasis and style.

• Он работает недостаточно быстро sounds very neutral.
• Он недостаточно быстро работает puts slightly more focus on недостаточно быстро.

Russian often moves words around for emphasis, but the meaning stays basically the same.

They are close, but not exactly identical.

• недостаточно быстро = not fast enough
• слишком медленно = too slowly

In many situations they mean nearly the same thing. But the viewpoint is a little different:

• недостаточно быстро focuses on failing to reach the needed speed
• слишком медленно focuses on excessive slowness

So:

• Он работает недостаточно быстро = He is not working fast enough.
• Он работает слишком медленно = He is working too slowly.

It can describe either one.

Depending on context, it may mean:

• a general characteristic:
  He doesn’t work fast enough.
• what is happening at the moment:
  He isn’t working fast enough right now.

Russian present tense with an imperfective verb often covers both meanings.

You would change both the pronoun and the verb form.

• Он работает недостаточно быстро. = He works / is working not fast enough.
• Она работает недостаточно быстро. = She works / is working not fast enough.
• Они работают недостаточно быстро. = They work / are working not fast enough.

Notice:

• он / она работает
• они работают

So the verb agrees with the subject.

The stress is:

• Он рабОтает недостаточно бЫстро.

More specifically:

• рабОтает
• недостАточно
• бЫстро

Stress matters in Russian, so it is worth learning each word with its stress pattern.