Я долго колебалась, но всё-таки записалась на курс.

Because both verbs are:

1. past tense
2. feminine singular
3. reflexive

1) Past tense

In Russian, past tense is formed with -л-:

• колебалась
• записалась

2) Feminine singular

The ending -а shows that the speaker is female:

• я колебалась = I hesitated, said by a woman
• A man would say:
  • Я долго колебался, но всё-таки записался на курс.

3) Reflexive

The -сь / -ся part is the reflexive marker.

So:

• колебалась = feminine past of колебаться
• записалась = feminine past of записаться

The short version: -ась here is basically -а (feminine past ending) + -сь (reflexive marker).

Yes. This is a very typical Russian aspect contrast.

• колебалась is imperfective
• записалась is perfective

колебалась = imperfective

This presents the hesitation as a process or something that lasted for some time:

• Я долго колебалась = I was hesitating for a long time

It focuses on the duration, not on a completed result.

записалась = perfective

This presents the act of signing up as a completed action with a result:

• записалась на курс = signed up for the course

So the sentence naturally means:

• first there was an extended period of hesitation,
• then a completed decision/action happened.

That is why this combination sounds very natural in Russian.

Долго is an adverb meaning for a long time.

It modifies колебалась:

• Я долго колебалась = I hesitated for a long time

It works especially well with the imperfective verb because imperfective verbs often describe duration, repetition, or process.

Compare:

• Я долго колебалась = I hesitated for a long time
• Я колебалась = I hesitated

So долго adds the idea that the indecision lasted.

Всё-таки adds the sense of:

• after all
• still
• nevertheless
• in the end

In this sentence, it shows that the final action happened despite the hesitation:

• но всё-таки записалась = but I signed up anyway / but in the end I did sign up

It often carries a feeling like:

• there was resistance,
• doubt,
• difficulty,
• but the action happened in spite of that.

So the sentence is stronger than just:

• Я долго колебалась, но записалась на курс.

Adding всё-таки makes the contrast more expressive.

Not really. They do related but slightly different jobs.

• но = but
• всё-таки = still / nevertheless / after all / in the end

So together:

• но всё-таки = but still / but nevertheless / but in the end

What each one contributes

• но marks the contrast
• всё-таки emphasizes that the action happened despite the previous hesitation

Without всё-таки, the sentence is grammatically fine, but a little less expressive:

• Я долго колебалась, но записалась на курс.

With всё-таки, the speaker sounds more like:

• I really hesitated, but I did end up signing up.

Because the verb записаться commonly uses the pattern:

• записаться на + accusative

This is the normal way to say sign up for / enroll in something such as:

• записаться на курс = sign up for a course
• записаться на занятия = sign up for classes
• записаться на приём = book/register for an appointment
• записаться на экзамен = register for an exam

Why курс looks unchanged

Курс is masculine inanimate singular, and in the accusative it looks the same as the nominative:

• nominative: курс
• accusative: курс

So even though it is accusative after на, the form does not change here.

It is in the accusative case.

The preposition на can take different cases depending on meaning, but after записаться на it normally takes the accusative:

• на курс
• на лекцию
• на урок
• на курсы

In this sentence:

• записаться на курс = to sign up for a course

As mentioned, курс happens to look the same in nominative and accusative because it is an inanimate masculine noun.

Historically and structurally, yes, that is a useful way to think about it.

In modern Russian, записаться is the normal verb for:

• sign up
• enroll
• register oneself

So:

• Я записалась на курс = I signed up for a course

The reflexive ending does not always need to be translated literally into English, but it is part of the standard verb.

Compare

• записать = to write down / record / enroll someone
• записать кого-то на курс = to sign someone up for a course
• записаться на курс = to sign oneself up / to sign up

So yes, the reflexive idea is real, but in English we usually just say sign up.

Yes, it is a normal verb, though it can sound a bit more formal or literary than some alternatives in certain contexts.

Колебаться means:

• to hesitate
• to waver
• to be undecided

It suggests going back and forth mentally, not being able to decide.

Similar verbs

• сомневаться = to doubt
• не решаться = to not dare / be unable to bring oneself to do something

These are related, but not identical.

For example:

• Я долго колебалась = I hesitated / wavered for a long time
• Я долго сомневалась = I had doubts for a long time
• Я долго не решалась записаться = I couldn’t bring myself to sign up for a long time

So колебалась focuses on indecision between options or possible actions.

Sometimes yes, if the context is clear:

• Долго колебалась, но всё-таки записалась на курс.

That can sound perfectly natural in conversation or narration.

However, Russian past tense verbs do not show person, only gender/number:

• колебалась = could mean I hesitated or she hesitated, depending on context

So including Я makes the subject completely explicit:

• Я долго колебалась...

In English, I is required. In Russian, it is often optional, but here it helps avoid ambiguity.

Yes. Russian word order is flexible, and changes in word order often affect emphasis more than basic meaning.

The original sentence:

• Я долго колебалась, но всё-таки записалась на курс.

Possible variations:

• Я всё-таки записалась на курс, хотя долго колебалась.
• Долго колебалась, но всё-таки я записалась на курс.
• На курс я всё-таки записалась, хотя долго колебалась.

These versions are all understandable, but the emphasis shifts.

Why the original sounds natural

It gives the events in a clear order:

1. hesitation
2. final action

So it feels very natural and neutral.

The main changes would be in the past-tense verb forms.

Male speaker

• Я долго колебался, но всё-таки записался на курс.

Female speaker

• Я долго колебалась, но всё-таки записалась на курс.

Plural

• Мы долго колебались, но всё-таки записались на курс.

So the past tense agrees with the subject in gender and number:

• masculine singular: -ся / -лся
• feminine singular: -ась / -лась
• plural: -ись / -лись