Завтра я встану рано, чтобы не опоздать на работу.

Встану is future tense.

It comes from the verb встать = to get up / to stand up.
This verb is perfective, and perfective verbs in Russian form the future with what look like present-tense endings:

• я встану
• ты встанешь
• он/она встанет

So although встану looks like a present form, it means I will get up.

Because встану fits a single completed action tomorrow morning.

Russian often contrasts:

• встать → perfective, one completed act: to get up
• вставать → imperfective, process, repetition, or habit: to be getting up / to get up regularly

So:

• Завтра я встану рано = tomorrow I’ll get up early once
• Я буду вставать рано = I’ll be getting up early / I’ll start getting up early regularly

In this sentence, the speaker means one specific action tomorrow, so встану is the natural choice.

They are related, but not the same.

• проснуться = to wake up
• встать = to get up (out of bed), or literally to stand up

So someone can:

• проснуться at 6:00
• but встать at 6:15

In this sentence, встану рано means the person will get up early, not just open their eyes.

Чтобы introduces a purpose clause. Here it means something like:

• so that
• in order to

So the structure is:

• Я встану рано, чтобы не опоздать...
• I’ll get up early so that I won’t be late...

It shows why the speaker will get up early.

Because the subject is the same person in both parts of the sentence.

• я встану
• and the same я is the one who does не опоздать

When the subject stays the same, Russian very often uses:

• чтобы + infinitive

So:

• Я встану рано, чтобы не опоздать.

If the subject were different, Russian would usually use a finite verb instead:

• Я встану рано, чтобы он не опоздал.
• I’ll get up early so that he won’t be late.

Because the sentence refers to one specific occasion: tomorrow’s trip to work.

• опоздать = perfective = to be late once / to arrive late
• опаздывать = imperfective = to be late regularly / to be in the habit of being late

So:

• чтобы не опоздать на работу = so as not to be late for work tomorrow
• чтобы не опаздывать на работу = so as not to keep being late for work in general

Here the speaker means one concrete event, so опоздать is right.

Because на работу is the normal Russian expression for to work / for work in this kind of context.

Russian commonly says:

• идти на работу = to go to work
• ехать на работу = to go/drive to work
• прийти на работу = to come to work
• опоздать на работу = to be late for work

This is just the standard idiomatic pattern.
For location, Russian uses:

• на работе = at work

So the contrast is:

• на работу = to work
• на работе = at work

Работу is accusative singular.

That is because на can take different cases depending on meaning:

• на работу = motion/direction → accusative
• на работе = location → prepositional

So in this sentence, the person is talking about being late to work, which uses the directional idea, hence на работу.

It could be omitted.

Russian often drops subject pronouns when the verb form already makes the subject clear.
Since встану clearly means I will get up, you could say:

• Завтра встану рано, чтобы не опоздать на работу.

That still sounds natural.

Including я is also normal. It can make the sentence a little clearer, fuller, or slightly more emphatic.

Yes, Russian word order is flexible.

Завтра is placed first here to set the time frame right away: tomorrow.
Other possible orders are:

• Я завтра встану рано, чтобы не опоздать на работу.
• Я встану завтра рано, чтобы не опоздать на работу.

These are all understandable, but the original word order sounds very natural and neutral.

Russian often moves words around for emphasis, topic, or rhythm more freely than English does.

Рано is an adverb, meaning early.

It modifies the verb встану:

• встану рано = will get up early

Because it is an adverb, it does not change for gender, number, or case.

Compare:

• ранний поезд = an early train → adjective
• встать рано = to get up early → adverb

Yes, in normal writing the comma is required.

That is because чтобы introduces a subordinate clause of purpose:

• Завтра я встану рано, чтобы не опоздать на работу.

Russian generally places a comma before conjunctions like что, чтобы, когда, если, etc. when they begin a subordinate clause.

So here the comma is standard and expected.