Learn Hardcore Russian: После прогулки в парке я успокаиваюсь.

So after после you must say после прогулки = after (the) walk.
It is genitive singular, not plural. The ending -и here marks genitive singular for a feminine noun in -ка.

How do I know прогулки is genitive singular and not nominative plural?

Formally, прогулки can be:

genitive singular: of the walk
nominative plural: walks

You understand which one it is from context and preposition:

после always takes genitive → here прогулки = genitive singular.
There is no reason for a plural here; the sentence is about a walk in the park as a type of situation, not a specific list of multiple walks.

So whenever you see после + прогулки, treat прогулки as genitive singular.

Why is it в парке and not в парк?

Because the meaning is during a walk *in the park (inside / within it), not *towards the park.

в парк (+ accusative) = movement into the park
- Я иду в парк. – I am going to the park.
в парке (+ prepositional) = location inside the park
- Я гуляю в парке. – I am walking in the park.

In после прогулки в парке, the idea is a walk that takes place in the park, so you need в парке (prepositional case of парк: парке).

Why is the verb успокаиваюсь and not just успокаиваю?

Успокаиваюсь has the reflexive ending -сь, which corresponds roughly to English myself in I calm myself (down).

успокаивать кого-то – to calm someone (else) down
- Я успокаиваю ребёнка. – I am calming the child down.
успокаиваться – to calm down (oneself, or to become calm)
- Я успокаиваюсь. – I calm down / I become calm.

In this sentence you are talking about your own state after a walk, so you need the reflexive verb: я успокаиваюсь.

What is the difference between успокаиваться and успокоиться?

They are an aspect pair:

успокаиваться – imperfective (process, repeated/habitual action)
- Я успокаиваюсь после прогулки.
  I calm down after a walk (habitually, in general).
успокоиться – perfective (single, completed result)
- Я успокоюсь после прогулки.
  I will calm down after the walk (one specific time / result).

In your sentence, успокаиваюсь is used as a general or habitual statement about what usually happens after a walk, so the imperfective is correct.

Is я успокаиваюсь present tense or future tense?

It is present tense of the imperfective verb успокаиваться:

я успокаиваюсь
ты успокаиваешься
он/она успокаивается
мы успокаиваемся
вы успокаиваетесь
они успокаиваются

Here it describes either:

What generally happens (habitual present):
After a walk in the park, I (usually) calm down.
What is happening now in a narrative sense:
After the walk in the park, I am calming down (now).

It is not future; the future would use the perfective успокоиться → я успокоюсь.

Could I say После того как я гуляю в парке, я успокаиваюсь instead?

You can, and it is grammatically correct, but it sounds more wordy and less natural than the original.

После прогулки в парке я успокаиваюсь.
– Compact and idiomatic: After a walk in the park, I calm down.
После того как я гуляю в парке, я успокаиваюсь.
– Literally: After the fact that I walk in the park, I calm down.
Grammatically fine, but heavier and unnecessarily clumsy in everyday speech.

Native speakers prefer после + noun (in genitive) in this kind of sentence.

Can I change the word order to Я успокаиваюсь после прогулки в парке?

Yes, that is perfectly correct and very natural.

После прогулки в парке я успокаиваюсь.
Я успокаиваюсь после прогулки в парке.

Both mean the same. Russian word order is fairly flexible. Differences:

Starting with После прогулки в парке slightly emphasizes the condition or time after which you calm down.
Starting with Я slightly emphasizes you or your state.

But in neutral context, they are practically interchangeable.

Do I need a comma anywhere in После прогулки в парке я успокаиваюсь?

No comma is needed.

It is a simple sentence with:

a prepositional phrase (adverbial modifier): После прогулки в парке
a subject: я
a predicate (verb): успокаиваюсь

There are no separate clauses here, so there is no reason to put a comma.

Could I say После прогулки по парку instead of в парке? Does it change the meaning?

Yes, you can say После прогулки по парку, and it is also correct, but the nuance changes slightly:

прогулка в парке – a walk in the park, focusing on the location (inside the park).
прогулка по парку – a walk around/through the park, focusing a bit more on movement within the park’s area.

In practice, both are often understood similarly, and in this sentence either is possible.
В парке is slightly more neutral; по парку adds a subtle sense of walking around the park’s paths/space.

Could I say После прогулок в парке я успокаиваюсь instead of После прогулки?

Yes, but the meaning shifts:

После прогулки в парке – after a walk in the park (one walk, or a walk as a general type of situation).
После прогулок в парке – after walks in the park (repeated occasions / many walks).

Both can be general statements, but:

Singular прогулки (genitive singular) sounds like “after a walk in the park, I (generally) calm down.”
Plural прогулок (genitive plural) makes you think more about multiple walks as events that often happen.

Why don’t we say я успокаиваю себя instead of я успокаиваюсь?

Russian usually prefers reflexive verbs with -сь instead of explicit себя for this kind of meaning.

я успокаиваюсь – I calm down / I calm myself (down).
я успокаиваю себя – grammatically possible, but sounds unusual and overly analytical, used only in very specific stylistic contexts.

So the natural, everyday way to say I calm myself is simply я успокаиваюсь.

How is успокаиваюсь pronounced and where is the stress?

The stress is on the а:

успокАиваюсь → [u-spa-KA-i-va-yus’]

Syllable breakdown:

у‑спо‑кА‑и‑ва‑юсь

Common learner mistake: putting stress later (e.g. успокаИваюсь). That is incorrect; keep it on кА.

Could I use расслабляюсь instead of успокаиваюсь? What is the difference?

You can say:

После прогулки в парке я расслабляюсь.

The difference in nuance:

успокаиваюсь – I calm down, become less anxious / less nervous, become emotionally and mentally calm.
расслабляюсь – I relax, loosen up physically and mentally, stop being tense.

They overlap, but:

If the focus is on reducing stress/anxiety → успокаиваюсь is better.
If the focus is on relaxing your body/feeling laid-back → расслабляюсь fits more.