A barátom szeretné, ha feltűnés nélkül érkeznénk.

Because Hungarian often uses the definite article before a possessed noun.

• barátom = my friend
• a barátom = still my friend

So the a here is not translated separately into English. It is just normal Hungarian grammar. In a neutral sentence like this, a barátom is the expected form.

Yes. The verb szeret basically means to like / to love, but in the conditional it very often means would like.

So:

• szereti = he/she likes it
• szeretné = he/she would like it

In this sentence, A barátom szeretné... means My friend would like...

This is softer and more natural than using akarja (wants), which sounds stronger and more direct.

Because this is the definite conjugation.

Hungarian verbs can have two kinds of endings:

• indefinite
• definite

Here, szeretné is the 3rd person singular conditional definite form of szeret.

Why definite? Because the verb has a definite content/object behind it. In sentences like this, Hungarian often treats the whole ha... clause as if there were an implied azt (that/it):

• A barátom szeretné [azt], ha...
• literally: My friend would like [it], if...

So szeretné is the natural form here.

Usually, yes: ha often means if.

But after verbs like szeretné, it is very common in Hungarian to use ha to introduce the thing someone wants or would like to happen.

So:

• A barátom szeretné, ha érkeznénk.
• literally: My friend would like it if we arrived.

In natural English, you may translate it more smoothly as:

• My friend would like us to arrive...

So in this pattern, ha still looks like if, but the whole structure means something more like would like it if... / would like ... to...

Because the subject changes.

Hungarian often uses an infinitive when the same person does both actions:

• A barátom szeretne korán érkezni.
• My friend would like to arrive early.

Here, however:

• my friend is the one who wants something
• we are the ones who would arrive

Since the subject of the second action is different, Hungarian normally uses a full clause:

• A barátom szeretné, ha érkeznénk.

That is one of the most important reasons this sentence is built this way.

Érkeznénk is the 1st person plural conditional form of érkezik (to arrive).

It means:

• we would arrive

Breakdown:

• érkez- = verb stem
• -ne- = conditional marker
• -nk = we

So:

• érkezünk = we arrive
• érkeznénk = we would arrive

In this sentence, it appears in the clause after ha, because that is the normal pattern after szeretné in this kind of meaning.

Because Hungarian normally uses the conditional in this kind of wish/desire structure:

• szeretné, ha... érkeznénk

The arrival is not presented as a fact. It is something the friend wants to happen. The conditional helps show that this is desired, not simply stated as real.

If you said érkezünk, that would sound much more like a plain factual we arrive / we are arriving, which does not fit this structure well.

Literally, it is something like:

• feltűnés = noticeability, conspicuousness, attracting attention
• nélkül = without

So feltűnés nélkül literally means without notice / without attracting attention / without being conspicuous.

A very natural English translation is:

• without attracting attention
• unobtrusively
• without being noticed

Also, nélkül is a postposition, so it comes after the noun:

• feltűnés nélkül
• not the other way around

Because Hungarian often uses a bare noun in this kind of expression, especially with abstract nouns and postpositions.

So:

• feltűnés nélkül = without attracting attention

This is a fixed, natural phrase. Adding an article would usually sound wrong here.

You can think of it as a general idea, not a specific piece of attention or conspicuousness.

That is the most neutral word order here.

In Hungarian, adverbial expressions like manner phrases often come before the verb in a neutral sentence:

• ha feltűnés nélkül érkeznénk

This gives a natural meaning like:

• if we arrived without attracting attention

Hungarian word order is flexible, but moving things around usually changes emphasis. The version in your sentence is the straightforward, unmarked order.