По утрам я быстро собираюсь, чтобы не опоздать на работу.

This is a fixed Russian pattern:

• по утрам = in the mornings
• по вечерам = in the evenings
• по понедельникам = on Mondays

Here по + plural dative often expresses a repeated time pattern.

So:

• утром = in the morning / this morning / in the morning in a general sense
• по утрам = mornings, as a habit

In this sentence, the speaker is talking about a routine, so по утрам is the natural choice.

Утрам is dative plural of утро.

That happens because the preposition по often takes the dative case, especially in expressions of habitual time like:

• по утрам
• по вечерам
• по выходным

So the structure is:

• по
  • dative plural = on / in / during ... regularly

In this sentence, собираюсь comes from собираться, which here means to get ready.

That is different from the non-reflexive собирать, which usually means to gather, to collect, or to assemble something.

Compare:

• Я собираю документы. = I collect the documents.
• Я собираюсь на работу. = I’m getting ready for work.

So the reflexive ending -сь is part of the verb’s normal form in this meaning.

Because the subject is я, so the verb must be 1st person singular, present tense.

The verb собираться conjugates like this:

• я собираюсь = I get ready / I am getting ready
• ты собираешься
• он/она собирается
• мы собираемся
• вы собираетесь
• они собираются

So я быстро собираюсь means I get ready quickly or I’m getting ready quickly, depending on context.

Быстро is an adverb, meaning quickly.

It describes how the action happens:

• я собираюсь = I get ready
• я быстро собираюсь = I get ready quickly

In Russian, adverbs often end in -о, like:

• быстро = quickly
• медленно = slowly
• хорошо = well

Here чтобы means so that or in order to.

It introduces a purpose clause:

• Я быстро собираюсь, чтобы не опоздать на работу.
• I get ready quickly so that I won’t be late for work.

So the second part explains why the speaker gets ready quickly.

Russian often uses чтобы + infinitive when the subject of both actions is the same person.

In this sentence:

• я собираюсь = I get ready
• (я) не опоздать = (for me) not to be late

Since the same person is involved, the infinitive is very natural.

If the subject changes, Russian more often uses a finite verb after чтобы:

• Я сказал ему, чтобы он пришёл рано.
• I told him to come early.

So чтобы не опоздать is a standard same-subject purpose construction.

This is an aspect question.

• опоздать = perfective = to be late (as a completed result)
• опаздывать = imperfective = to be late repeatedly / to be in the process of being late / to have a habit of being late

Here the speaker wants to avoid a specific result: arriving late. That is why Russian uses the perfective:

• чтобы не opоздать = so as not to be late

This is very common after чтобы when talking about a goal or desired result.

На работу is the standard Russian way to say to work when talking about going to one’s workplace.

• на работу = to work
• с работы = from work
• на работе = at work

Even though English uses to, Russian uses на here idiomatically.

So:

• идти на работу = to go to work
• опоздать на работу = to be late for work

You usually just have to learn this as a set expression.

Работу is accusative singular of работа.

That is because на takes the accusative when it shows movement toward a destination:

• на работу = to work

Compare that with location:

• на работе = at work

So:

• куда? (where to?) → на работу
• где? (where?) → на работе

Because чтобы introduces a subordinate clause of purpose, and Russian normally separates that clause with a comma.

So:

• Я быстро собираюсь, чтобы не опоздать на работу.

This is standard Russian punctuation.

Russian verbs usually show the subject clearly, so собираюсь already means I get ready.

However, Russian often still includes the pronoun:

• for clarity
• for emphasis
• just because it sounds natural in context

So both are possible:

• По утрам быстро собираюсь...
• По утрам я быстро собираюсь...

Including я is completely normal.

Yes. Russian word order is flexible, although different orders can sound more natural in different contexts.

Original:

• По утрам я быстро собираюсь, чтобы не опоздать на работу.

Possible variations:

• Я по утрам быстро собираюсь, чтобы не опоздать на работу.
• Быстро я по утрам собираюсь, чтобы не опоздать на работу. (more marked/emphatic)
• Чтобы не опоздать на работу, я по утрам быстро собираюсь.

The original order is natural and neutral: it starts with the time expression, then the subject, then the manner, then the purpose.

It can mean either, depending on context.

Russian present tense often covers both:

• I get ready
• I am getting ready

Since по утрам shows a repeated habit, the best English translation here is usually:

• In the mornings, I get ready quickly so I won’t be late for work.

So in this sentence, it is mainly habitual present, not a one-time action.