Learn Hardcore Russian: Психотерапевт помогает мне успокаиваться вечером. - The psychotherapist helps me calm down in the evening.

кому? (to whom?) → мне, тебе, ему, ей, нам, вам, им
So: Психотерапевт помогает мне… = The psychotherapist helps me… (literally: helps to me).

Using меня would be wrong here, because меня is accusative/genitive, and помогать does not use that case for the person being helped.

Why is успокаиваться reflexive? Could we say успокаивать instead?

Успокаиваться is reflexive because the subject calms themselves down.

успокаивать (кого?) – to calm someone else down
- Психотерапевт успокаивает клиента. – The therapist calms the client down.
успокаиваться – to calm down oneself, to become calm
- Я успокаиваюсь. – I calm down / I am calming down.

In Психотерапевт помогает мне успокаиваться, you are the one becoming calm, so the reflexive form успокаиваться is correct.
Успокаивать would mean the therapist is helping you calm someone else.

What is the difference between успокаиваться and успокоиться?

They are two aspects of the same verb:

успокаиваться – imperfective: process, repeated action, duration
- Он помогает мне успокаиваться. – He helps me calm down (in general / as an ongoing process).
успокоиться – perfective: one-time result, the moment you become calm
- Он помогает мне успокоиться. – He helps me (finally) calm down / reach a calm state (usually in a specific situation).

In your sentence, успокаиваться suggests a general, repeated, or ongoing process of calming down in the evenings.
If you said помогает мне успокоиться вечером, it would focus more on reaching calmness on a particular evening or as a single result.

How would I say in the evenings (regularly) instead of just in the evening?

Use вечерами for a habitual, repeated action:

Психотерапевт помогает мне успокаиваться вечером.
→ The therapist helps me calm down in the evening (this evening / in the evening in general, context-dependent).
Психотерапевт помогает мне успокаиваться вечерами.
→ The therapist helps me calm down in the evenings (on evenings in general, as a routine).

So вечером = in the evening (singular time reference; can be generic)
вечерами = in the evenings (plural, emphasizes regularity).

Why is вечером used without a preposition? In English we say in the evening.

Many Russian time expressions use a bare case form (often the instrumental) with no preposition. Вечером is the instrumental of вечер and functions adverbially:

утром – in the morning
днём – in the daytime / in the afternoon
вечером – in the evening
ночью – at night

So помогает мне успокаиваться вечером literally is like helps me calm down evening-time. No preposition is needed here.

Can I change the word order? For example, can I say Психотерапевт вечером помогает мне успокаиваться?

Yes. Russian word order is relatively flexible, and your example is natural:

Психотерапевт помогает мне успокаиваться вечером.
Психотерапевт вечером помогает мне успокаиваться.
Вечером психотерапевт помогает мне успокаиваться.

All are grammatically correct. The differences are mostly about emphasis:

Starting with Вечером highlights when it happens.
Putting вечером right after психотерапевт slightly emphasizes what the therapist does in the evening.

The original word order is neutral and very common.

Could I drop мне and just say Психотерапевт помогает успокаиваться вечером?

You can, but the meaning changes.

Психотерапевт помогает мне успокаиваться вечером.
→ The therapist helps me calm down in the evening.
Психотерапевт помогает успокаиваться вечером.
→ The therapist helps (people) calm down in the evening / helps with calming down in the evening (in general, no specific person mentioned).

Without мне, it sounds more general or impersonal, not clearly about you.

In English I’d say is helping me. Does помогает mean helps or is helping?

In Russian there is no separate present continuous form. Помогает can mean both:

Психотерапевт помогает мне успокаиваться вечером.
- He helps me calm down in the evening.
- He is helping me calm down in the evenings.

Context decides whether it sounds like a general fact or something ongoing right now; the Russian form is the same.

How would I say my psychotherapist instead of just the psychotherapist?

Add a possessive pronoun:

Мой психотерапевт помогает мне успокаиваться вечером.
→ My psychotherapist helps me calm down in the evening.

Russian has no articles (a / the), so психотерапевт by itself can be understood as a psychotherapist or the psychotherapist, depending on context. To be explicit that this is your therapist, use мой (if you are talking about your own):

мой психотерапевт – my (male) psychotherapist, or neutral if you don’t specify gender
colloquial feminine form: моя психотерапевтка – my female psychotherapist (style-dependent).

How is психотерапевт pronounced and where is the stress?

Stress is on -тев-:

психотерапевт → [психотерапЕвт]

Syllable breakdown: пси-хо-те-ра-певт
The stressed vowel is е in -певт. The initial психо- is like psycho- in English, but with Russian sounds:

пс is pronounced together: [пс], not пыс
х is a hard kh sound, as in German Bach or Scottish loch.

Why does успокаиваться end in -ться, not -тся?

This is a spelling rule for reflexive verbs:

The infinitive and imperative forms use -ться with a soft sign ь:
- успокаиваться, умыться, одеться
Finite present/past forms use -тся (no soft sign), when the verb ending would be -т:
- он успокаивается, он умывается, он одевается

In your sentence, успокаиваться is an infinitive (after помогает), so it must be spelled with -ться.

Could I use расслабиться instead of успокаиваться? What’s the difference?

You can, but the nuance changes.

успокаиваться – to calm down emotionally; reduce anxiety, agitation, stress.
расслабиться – to relax physically or mentally; stop being tense.

Compare:

Психотерапевт помогает мне успокаиваться вечером.
→ Focus on becoming calmer emotionally in the evenings.
Психотерапевт помогает мне расслабиться вечером.
→ Focus more on relaxing / unwinding in the evening (could be emotional or physical).

Both are possible; which is better depends on what you want to emphasize.