Learn Hardcore Russian: Я не помню, кого я встретил в парке.

Кого is the object form (accusative/genitive) of кто (“who”).
In English you would use whom as the object, but in everyday English most people just say who:

Russian: Я не помню, кого я встретил в парке.
Very literal English: I don’t remember whom I met in the park.
Normal English: I don’t remember who I met in the park.

Russian still keeps the case ending, so you must use the object form кого, not the nominative кто, because it is the direct object of встретил:

(Я) встретил кого? → кого (accusative).

What would the direct question be, and how does it turn into this sentence?

The corresponding direct question is:

Кого ты встретил в парке? – Whom did you meet in the park? / Who did you meet in the park?

To make the indirect question (object clause) used in your sentence, Russian keeps:

the same question word кого
the same case (still object)
almost the same word order

Then you just put it after a verb like я не помню (“I don’t remember”):

Я не помню, кого я встретил в парке.
Literally: I don’t remember whom I met in the park.

So:
Кого ты встретил в парке? → Я не помню, кого я встретил в парке.

Why is there a comma after помню?

In Russian, you normally put a comma before a subordinate clause introduced by words like кто, что, где, когда, почему, как, ли etc.

Here, кого я встретил в парке is a subordinate clause that functions as the object of я не помню:

Main clause: Я не помню
Subordinate (object) clause: кого я встретил в парке

Therefore Russian writing rules require a comma:

Я не помню, кого я встретил в парке.

In English we do not put a comma in this kind of sentence, but in Russian you must.

Can I omit the second я and just say Я не помню, кого встретил в парке?

Yes, that is perfectly correct and very natural:

Я не помню, кого встретил в парке.

When the subject of the subordinate clause is the same as the subject in the main clause (я here), Russian often drops the repeated pronoun. Both versions are grammatical:

Я не помню, кого я встретил в парке. – slightly more explicit / emphatic я
Я не помню, кого встретил в парке. – more compact, very common in speech and writing

As a learner, you can safely use the shorter version; just remember that the implied subject is still я.

Why is it встретил and not встречал?

This is about aspect: встретил (perfective) vs встречал (imperfective).

встретил – a single, completed event; you met someone once (result is important)
встречал – repeated / habitual action or an ongoing process; “used to meet”, “was meeting”

With не помню and a specific event, Russian naturally uses the perfective:

Я не помню, кого я встретил в парке.
“I don’t remember (the person I once met in the park).”

If you said:

Я не помню, кого я встречал в парке.

it would suggest something like “I don’t remember whom I (used to) meet in the park” – more about habitual or repeated meetings, not one occasion.

Why is встретил masculine, and what changes if the speaker is female?

In Russian, past-tense forms agree with the gender of the subject, even in the 1st person singular:

Masculine speaker: я встретил
Feminine speaker: я встретила

So, as written, the sentence assumes a male speaker:

(Мужчина): Я не помню, кого я встретил в парке.

If the speaker is female, you should say:

(Женщина): Я не помню, кого я встретила в парке.

Everything else in the sentence stays the same; only the past-tense ending changes to mark the gender of я.

Can I use встретился here instead of встретил? What is the difference?

Встретить кого and встретиться с кем are similar but not identical:

встретить кого (perfective) – to meet someone, often by chance; focuses on you encountering them
- Я встретил друга в парке. – I met (ran into) my friend in the park.
встретиться с кем (perfective reflexive) – to meet with someone, often arranged / mutual
- Я встретился с другом в парке. – I met up with my friend in the park.

So your sentence with встретиться would be:

Я не помню, с кем я встретился в парке.

Note the changes:

verb: встретился (reflexive)
preposition + case: с кем (instrumental), not кого (accusative)

Meaning shifts from “whom I (happened to) meet” to “with whom I met up.”

Why is it в парке and not в парк (or на парке)?

Russian uses в with different cases depending on meaning:

в + prepositional (в парке) → location: где? (where?)
- Я встретил его в парке. – I met him in the park.
в + accusative (в парк) → direction: куда? (where to?)
- Я пошёл в парк. – I went to the park.

In your sentence, the action happens in the park (location), not movement to the park, so you need prepositional:

в парке – “in the park”

You do not say на парке. The usual preposition for park is в: в парке.

How flexible is the word order in кого я встретил в парке?

Russian word order inside the clause is relatively flexible, but there is a neutral order that sounds most natural:

Neutral: кого я встретил в парке

Other variants are possible and can add emphasis:

кого я в парке встретил – slight emphasis on “in the park”
в парке кого я встретил – strong focus on “in the park” (more literary / expressive)
кого встретил я в парке – emphasizing я or giving the clause a more emotional / poetic feel

As a learner, it’s safest to stick to:

кого я встретил в парке (or кого встретил в парке if you drop я)

This is natural, clear, and neutral.

What is the difference between Я не помню, кого я встретил в парке and Я забыл, кого я встретил в парке?

Both can be translated “I don’t remember whom I met in the park”, but the nuance is different:

Я не помню… – I don’t remember (now).
Focus on your current state: the information is not in your memory at the moment. You may or may not have forgotten it; you just don’t remember.
Я забыл… – I forgot…
Implies that you used to know (you remembered before) but then lost that memory. It focuses on the act of forgetting in the past.

In many everyday situations they can be used in similar contexts, but:

If you simply want to state that you don’t know / don’t remember at the moment, Я не помню, кого я встретил в парке is the most neutral choice.