Haluan maata sohvalla.

It is built into maata.

In Finnish, the basic dictionary form of a verb is the first infinitive, and that form often corresponds to English to + verb.

So:

• haluan = I want
• maata = to lie
• haluan maata = I want to lie

Finnish does not use a separate word like English to here.

Because haluan already tells you the subject is I.

The ending -n marks first person singular, so haluan means I want.

That is why Finnish often leaves out the subject pronoun when it is clear:

• Haluan maata sohvalla. = I want to lie on the sofa.

You can add minä for emphasis or contrast:

• Minä haluan maata sohvalla, mutta hän haluaa istua.
  I want to lie on the sofa, but he/she wants to sit.

Because after haluta (to want), Finnish normally uses the infinitive of the next verb.

So:

• haluan maata = I want to lie

Not:

• haluan makaan
• haluan makaa

Those are not correct here.

A useful thing to know is that this verb changes its stem when conjugated:

• maata = to lie
• minä makaan = I am lying / I lie
• hän makaa = he/she is lying

So the infinitive maata and the present-tense forms makaan, makaa look different, which can surprise learners.

Usually maata means to be lying or to lie in a reclining position.

So Haluan maata sohvalla most naturally means that you want to be lying on the sofa.

It does not primarily mean to go and lie down. If you want to emphasize movement into that position, Finnish often uses another structure, for example:

• Haluan mennä sohvalle makaamaan. = I want to go lie down on the sofa.

So maata focuses more on the state/position than the movement into it.

No, not in this sentence.

Here maata is clearly a verb infinitive because it follows haluan.

That said, maata can also be a form of the noun maa in other contexts, so learners sometimes notice the spelling and get confused. But in:

• Haluan maata sohvalla

it can only reasonably be understood as to lie.

Because Finnish uses a case ending instead of a separate preposition like English on.

• sohva = sofa
• sohvalla = on the sofa / at the sofa

The ending -lla/-llä is called the adessive case, and it often expresses meanings like on, at, or by.

So:

• Haluan maata sohvalla.
  = I want to lie on the sofa.

Because sohvalla means on the sofa, which is the normal idea here.

Compare:

• sohvalla = on the sofa
• sohvassa = in the sofa

For a normal sofa situation, Finnish uses -lla, not -ssa, because you are understood as being on the piece of furniture, not physically inside it.

So sohvassa would sound strange in most everyday situations.

These are three very useful location forms:

• sohvalla = on the sofa
• sohvalle = onto the sofa / to the sofa
• sohvalta = off the sofa / from the sofa

Examples:

• Makaaan sohvalla. = I am lying on the sofa.
• Menen sohvalle. = I go onto the sofa.
• Nousen sohvalta. = I get up from the sofa.

In your sentence, sohvalla is used because the idea is location: being on the sofa.

Yes, you could, but the meaning is slightly different.

• Haluan maata sohvalla. = I want to lie on the sofa.
• Haluan olla sohvalla. = I want to be on the sofa.

The version with maata specifically tells us the person wants to be in a lying/reclining position.

The version with olla is more general. You are just saying you want to be there, without focusing on posture.

So if posture matters, maata is better.

The neutral, most natural order is:

• Haluan maata sohvalla.

Finnish word order is fairly flexible, but changing it usually adds emphasis.

For example:

• Sohvalla haluan maata.

This is possible, but it sounds more marked, as if you are emphasizing on the sofa rather than somewhere else.

So for a learner, Haluan maata sohvalla is the best standard pattern to use.