A barátom és én segítünk egymásnak.

Because Hungarian normally uses the definite article before a possessed noun too. So a barátom is the normal full phrase for my friend.

It does not translate word for word as the my friend. That is just standard Hungarian structure.

Also:

• a is used before a consonant: a barátom
• az is used before a vowel: az anyám

It is:

• barát = friend
• -om = my

So barátom literally means friend-my, which Hungarian uses for my friend.

The ending is -om because of Hungarian vowel harmony and the shape of the noun.

That is true in many sentences. Hungarian often leaves out subject pronouns because the verb ending already shows the person.

But here the speaker wants to say exactly who we are: my friend and I. The verb segítünk tells you we help, but it does not tell you which people make up that we.

So:

• Segítünk egymásnak. = We help each other.
• A barátom és én segítünk egymásnak. = My friend and I help each other.

Because the subject includes the speaker.

In Hungarian, if the subject is X and I, the verb is first person plural, because that means we. So:

• a barátom és én = my friend and I
• therefore the verb must be segítünk = we help

Segítenek would mean they help, so it would not match én.

It is made from:

• segít = help
• -ünk = we

So segítünk means we help.

More specifically, this is the first person plural indefinite form. Hungarian has two main conjugation patterns, often called indefinite and definite. Here the indefinite form is used because there is no definite direct object after the verb.

Because segít commonly goes with the dative pattern:

• segít valakinek = help someone

So each other appears here in the dative:

• egymásnak = to each other

Compare:

• Szeretjük egymást. = We love each other.
  Here egymást is accusative, because szeret takes a direct object.

• Segítünk egymásnak. = We help each other.
  Here egymásnak is dative, because segít is being used with valakinek.

You may sometimes encounter segít with an accusative object too, especially in modern usage, but for learners this dative pattern is the safest and most standard one to learn.

Yes, it is one word.

It breaks down as:

• egymás = each other / one another
• -nak = dative ending, roughly to or for

So egymásnak means to each other.

Hungarian often adds case endings directly onto words like this instead of using separate prepositions.

Yes. Hungarian word order is flexible, and different orders can change what is emphasized.

Your sentence:

• A barátom és én segítünk egymásnak.

is a natural, neutral way to say it.

Other possibilities include:

• Egymásnak segítünk.
  Stronger emphasis on each other

• Segítünk egymásnak.
  The subject is omitted because it is understood

So the sentence you have is not the only possible order, but it is a very normal one.

Both are grammatical.

But A barátom és én often sounds a bit more natural or polite, much like English speakers often prefer my friend and I over I and my friend.

Putting én first is possible, but it can sound a little more self-focused depending on context.

Yes. Barátom can mean either:

• my friend
• my boyfriend

Context usually makes the meaning clear.

So if you saw A barátom és én... by itself, it could in some situations mean My boyfriend and I... But if the meaning has already been given to you as my friend and I, then that is the intended reading here.

A rough guide:

• barátom → BA-raa-tom
• segítünk → roughly sheh-GEE-tünk
• egymásnak → roughly edy-MAAsh-nok

A few useful sound notes:

• á = a long a, somewhat like the vowel in father
• é = a long e, somewhat like ay, but smoother
• s in Hungarian sounds like English sh
• gy is a soft consonant, roughly like dy
• ü has no exact English equivalent; it is like German ü or French u

Also, Hungarian stress is normally on the first syllable of the word.