A barátom szeretné, ha feldíszítenénk és berendeznénk a szobát.

In a normal Hungarian sentence, a specific possessed noun often takes the definite article.

So:

• a barátom = my friend in a neutral sentence
• barátom without a sounds incomplete or belongs to a special style or context

For example:

• A barátom megérkezett. = My friend arrived.
• Barátom! = My friend! / Friend! (addressing someone)

So in your sentence, a barátom is the natural subject form.

barátom consists of:

• barát = friend
• -om = my

So literally it is friend-my.

Hungarian usually marks possession on the noun itself, instead of using a separate word like my before it.

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

• szeret = likes/loves
• szeretne = would like
• szeretné = would like it / would want it

In this sentence, szeretné is the normal form used before a ha clause.

A useful pattern to remember is:

• szeretné, ha... = would like it if... / would like someone to...

So it is best to learn szeretné, ha... as a set structure.

This is because Hungarian commonly uses the definite form in the pattern szeretné, ha...

You can think of it as if there were an implied azt = that/it:

• A barátom azt szeretné, ha...
  = My friend would like it that/if...

Even when azt is not actually said, the verb often stays in the definite form: szeretné.

So for learners, the safest rule is:

• memorize szeretné, ha...
• don’t try to use szeretne, ha... here in standard usage

Yes, ha usually means if, but after szeretné it forms a very common Hungarian pattern:

• szeretné, ha...

Literally, this is something like:

• would like it if...

In natural English, though, we often translate it more smoothly as:

• would like us to...
• would like someone to...

So although ha looks like if, this is not really an ordinary condition like if it rains. It is part of a fixed wish/desire structure.

As for hogy: Hungarian often uses hogy for that, but after szeretné with a different subject, the usual standard pattern is ha, not hogy.

Because after szeretné, ha..., Hungarian normally uses the conditional mood in the subordinate clause.

So:

• feldíszítenénk = we would decorate
• berendeznénk = we would furnish/arrange

In this sentence, the conditional does not mainly express uncertainty. It is the normal grammar after szeretné, ha... to express a desired action.

This is one of those places where Hungarian grammar works differently from English. English often uses:

• would like us to decorate...

Hungarian instead uses:

• szeretné, ha feldíszítenénk...

Because both verbs end in -nénk, which marks 1st person plural conditional:

• feldíszítenénk = we would decorate
• berendeznénk = we would furnish/arrange

Hungarian usually does not need a separate subject pronoun like mi = we, because the verb ending already tells you the person and number.

So there is no need to say mi feldíszítenénk unless you want extra emphasis.

These are verbal prefixes, and they often change the meaning in an important way.

• díszíteni = to decorate

• feldíszíteni = to decorate fully, to put up decorations, to make festive

• rendezni = to arrange, organize
• berendezni = to furnish, fit out, arrange the interior of a room

So the prefixes are not just random extras. They help create the specific meanings needed here.

In particular:

• feldíszíteni often suggests decorative finishing
• berendezni often suggests setting up a room with furniture or arranging its interior

Because a szobát is the direct object of the verbs.

• a szoba = the room
• a szobát = the room (object form)

The -t is the accusative ending.

Both verbs share the same object:

• decorate the room
• furnish/arrange the room

So Hungarian says the object once, at the end:

• feldíszítenénk és berendeznénk a szobát

Not if the meaning is that we would do it.

Compare:

• A barátom szeretné, ha feldíszítenénk és berendeznénk a szobát.
  = My friend would like us to decorate and furnish the room.

• A barátom szeretné feldíszíteni és berendezni a szobát.
  = My friend would like to decorate and furnish the room.

So:

• if the subject is different, Hungarian often uses szeretné, ha...
• if the subject is the same, Hungarian can use the infinitive

That is an important difference.

The word order is not completely fixed, but the version you have is very natural and neutral.

Current structure:

• A barátom = topic
• szeretné = main verb
• ha feldíszítenénk és berendeznénk a szobát = subordinate clause

Inside the subordinate clause, placing a szobát at the end works well because it is the shared object of both verbs.

You could also say:

• A barátom szeretné, ha a szobát feldíszítenénk és berendeznénk.

That puts more emphasis on the room.

So the meaning stays similar, but the emphasis changes.

Because ha feldíszítenénk és berendeznénk a szobát is a subordinate clause.

Hungarian normally separates this kind of clause from the main clause with a comma:

• A barátom szeretné, ha...

So the comma is standard punctuation here.

Not exactly.

berendezni is often stronger and more specific than plain arrange. It often means:

• to furnish
• to fit out
• to set up the interior of a room
• to arrange a room so it is properly equipped

So in a sentence about a room, berendezni often suggests more than just moving things around. It can imply making the room properly set up or furnished.