Бег по утрам помогает мне меньше нервничать.

Бег is a noun meaning running as an activity or form of exercise.

So:

• Бег по утрам = running in the mornings / morning running
• Бегать по утрам = to run in the mornings

In this sentence, Russian chooses the noun phrase as the subject:

• Бег по утрам помогает... = Running in the mornings helps...

If you used a verb instead, you would need a different structure, for example:

• Бегать по утрам помогает мне меньше нервничать.

That is also possible in Russian, but бег по утрам sounds a bit more like the practice/habit of morning running.

По утрам means in the mornings or every morning / mornings in general.

It expresses a repeated time pattern, not one specific morning.

Compare:

• утром = in the morning / this morning / one morning, depending on context
• по утрам = in the mornings, regularly or habitually

So:

• Я бегаю утром. = I run in the morning / I am running this morning (context decides)
• Я бегаю по утрам. = I run in the mornings (habit)

Because the expression по утрам requires the dative plural form.

The noun is:

• dictionary form: утро = morning
• dative plural: утрам

This is part of a common Russian time expression pattern:

• по утрам = in the mornings
• по вечерам = in the evenings
• по выходным = on weekends
• по понедельникам = on Mondays

You do not usually translate this word-for-word. It is best learned as a fixed pattern meaning on / in ... regularly.

The verb помогать / помочь takes the person receiving help in the dative case.

So:

• помогает мне = helps me
• помогает тебе = helps you
• помогает ему = helps him

This is different from English, where we just say helps me without thinking about case.

A few examples:

• Музыка помогает мне расслабиться. = Music helps me relax.
• Сон помогает детям расти. = Sleep helps children grow.

So in your sentence, мне is correct because running helps me.

After помогать meaning to help, Russian often uses an infinitive to say help someone do something.

Pattern:

• что-то помогает кому-то + infinitive

Examples:

• Чай помогает мне заснуть. = Tea helps me fall asleep.
• Спорт помогает людям чувствовать себя лучше. = Sport helps people feel better.
• Бег по утрам помогает мне меньше нервничать. = Running in the mornings helps me worry less.

So нервничать is in the infinitive because it means to be nervous / to get stressed / to worry as the action being helped.

With verbs, Russian usually uses меньше to mean less.

So:

• меньше нервничать = to worry less
• меньше есть = to eat less
• меньше работать = to work less

Менее is more formal and is more often used with adjectives, adverbs, or in more bookish language:

• менее важный = less important
• менее интересно = less interesting

So меньше нервничать is the natural everyday choice.

Нервничать means to be nervous, to get stressed, to worry, or to feel tense, depending on context.

In this sentence, it is something like:

• to feel less stressed
• to be less anxious
• to worry less

It does not always mean clinical anxiety; very often it just means everyday nervousness or stress.

Examples:

• Я нервничаю перед экзаменом. = I’m nervous before the exam.
• Не нервничай. = Don’t worry / Don’t be nervous.

Because the subject is бег, and бег is a singular masculine noun.

So the verb agrees with бег:

• бег помогает = running helps

If the subject were plural, the verb would be plural too:

• Упражнения помогают мне меньше нервничать. = Exercises help me worry less.

Here the core subject is not утрам. The subject is бег.
По утрам is only a time expression attached to it.

Yes. Russian word order is flexible, though different orders can sound more natural depending on what you want to emphasize.

The original sentence:

• Бег по утрам помогает мне меньше нервничать.

Other possible versions:

• По утрам бег помогает мне меньше нервничать.
• Мне помогает меньше нервничать бег по утрам.

The original version is the most neutral and natural for introducing the idea.
Moving по утрам to the front can emphasize the time/habit.

Yes, but the meaning changes.

• Бег утром помогает мне меньше нервничать. = Running in the morning helps me worry less.
  • This can sound more general, or refer to morning as a time of day.
• Бег по утрам помогает мне меньше нервничать. = Running in the mornings helps me worry less.
  • This clearly suggests a regular habit.

So по утрам is better if you mean as a routine.

Grammatically yes, but it is much less natural here.

• бег is the normal, common noun for running
• бегание is a verbal noun formed from the verb, but it often sounds heavier, more technical, or less idiomatic

So:

• Бег по утрам = natural
• Бегание по утрам = possible, but awkward in everyday speech

Learners often try to build nouns from verbs, but Russian frequently already has a simpler noun that sounds better.

Yes. Нервничать is imperfective, and that fits the meaning well.

The sentence is about a general effect or ongoing tendency:

• running in the mornings helps me be less stressed / worry less

Russian normally uses the imperfective infinitive after помогает when talking about a repeated or general result.

A perfective form would not fit as naturally here.
There is a related verb понервничать (to be nervous for a while), but that would express a more limited, one-time episode, which is not what this sentence means.

So меньше нервничать is the natural choice.