Learn Hardcore Russian: Я показал учителю черновик, и мне удалось получить полезный совет. - I showed the teacher the draft, and I managed to get useful advice.

Показал is perfective past: it presents the action as a single, completed event (I showed the draft once / finished showing it).
Показывал would be imperfective past, suggesting repetition, process, or background context (e.g., I was showing / I used to show drafts).

How does the verb показать “work” here—why are there two objects?

Показать commonly uses the pattern показать кому что = to show something to someone.
So:

учителю = to the teacher (dative case, “recipient”)
черновик = (the) draft (accusative case, “thing shown”)

Why is учителю in the dative case?

Because with показать, the person you show something to is marked with the dative (кому?).
учитель → учителю is the dative singular form.

Why is черновик in the accusative case?

It’s the direct object of показал: what was shown (что?).
For most inanimate masculine nouns, the accusative singular looks the same as the nominative: черновик.

Could the word order be different? For example, Я показал черновик учителю.

Yes. Russian word order is flexible and often changes emphasis:

Я показал учителю черновик: slightly highlights the teacher as the recipient (who you showed it to).
Я показал черновик учителю: slightly highlights the draft (what you showed). Both are natural; context decides what sounds best.

Why is there a comma before и?

Because this sentence joins two independent clauses: 1) Я показал учителю черновик
2) мне удалось получить полезный совет
When и connects two full clauses, Russian typically uses a comma.

What does мне удалось mean grammatically? Why isn’t it я удалось?

Мне удалось is an impersonal construction meaning I managed / I succeeded (in...).
Literally it’s like “To me it succeeded”, so the person is in the dative (мне, not я). This is a common Russian way to express success that “happened” to someone.

Why is удалось neuter past (-лось)?

In impersonal constructions, there is no real grammatical subject, so Russian often uses the neuter singular past form: удалось (from удаться).
It stays the same regardless of who succeeded: мне удалось, ему удалось, нам удалось, etc.

Why do we use the infinitive получить after удалось?

Удаться typically combines with an infinitive to express managing to do something:
удалось + infinitive = managed to + verb
So мне удалось получить = I managed to get/obtain.

Could it be получать instead of получить?

Usually получить (perfective) is preferred here because удалось points to a successful result—you achieved it.
получать (imperfective) would sound unusual in this exact meaning, unless you mean something like “managed to be receiving (regularly)” in a specific context.

Why is полезный совет in the accusative?

Because совет is the direct object of получить (получить что?).
So it’s accusative: полезный совет. (For an inanimate masculine noun, accusative = nominative in form.)

If the speaker were female, what changes?

Only the past-tense verb that agrees with the speaker’s gender changes:

Male speaker: Я показал...
Female speaker: Я показала... The rest (мне удалось...) stays the same.