Quiero ordenar mi escritorio antes de estudiar.

Because after querer when you say you want to do something, Spanish uses an infinitive.

• quiero estudiar = I want to study
• quiero ordenar = I want to tidy / organize

Estudio is a conjugated form meaning I study, so quiero estudio would be incorrect here.

Here, ordenar means to tidy, to organize, or to put in order.

So ordenar mi escritorio means something like:

• to tidy my desk
• to organize my desk

Be careful: ordenar can also mean to order in other contexts, but in this sentence it clearly means putting the desk in order.

Spanish often uses a possessive like mi when talking about something that belongs to you and needs to be clearly identified.

• mi escritorio = my desk

Using el escritorio would mean the desk, which is less specific. If you are talking about your own desk, mi escritorio is the natural choice.

Yes. In fact, Spanish usually leaves it out unless you want emphasis or contrast.

• Quiero ordenar mi escritorio antes de estudiar. = normal
• Yo quiero ordenar mi escritorio antes de estudiar. = more emphatic, like I want to tidy my desk

The verb form quiero already tells us the subject is I.

Because antes de is the normal structure before a noun or an infinitive.

• antes de estudiar = before studying / before I study
• antes de la cena = before dinner

When Spanish uses a verb after antes de, that verb stays in the infinitive if the subject does not need to be stated separately.

Good question. Both can relate to before studying, but they are used differently.

• antes de estudiar: uses an infinitive
• antes de que estudie: uses a conjugated verb after de que

Use antes de + infinitive when the subject is understood and usually the same as the main subject:

• Quiero ordenar mi escritorio antes de estudiar. = I want to tidy my desk before studying.

Use antes de que + subjunctive when you want to express a separate or explicit subject:

• Quiero ordenar mi escritorio antes de que llegue mi hermano. = I want to tidy my desk before my brother arrives.

Because that is a very natural Spanish word order.

The sentence is structured like this:

• Quiero = I want
• ordenar mi escritorio = to tidy my desk
• antes de estudiar = before studying

Spanish often puts time expressions like antes de estudiar after the main idea. You could move parts around for emphasis in some contexts, but this version is the most neutral and natural.

Yes, depending on the exact meaning.

• ordenar mi escritorio = tidy / put in order
• organizar mi escritorio = organize, often with a stronger sense of arranging things systematically
• arreglar mi escritorio = could work in some contexts, but arreglar often means fix, sort out, or tidy up depending on context

In Spain, ordenar mi escritorio sounds very natural for tidying my desk.

In this sentence, yes: escritorio means desk.

In some contexts, related words can be confusing:

• escritorio = desk
• despacho = office / study
• oficina = office

So here, mi escritorio is the piece of furniture, not the room.

Yes. English and Spanish do not always match word for word here.

• antes de estudiar can be translated as before studying
• depending on context, it can also sound natural in English as before I study

Spanish often uses the infinitive where English might choose either the -ing form or a full clause.

Yes, it is completely natural and correct in Spain.

It sounds like something a student might say in everyday life:

• Quiero ordenar mi escritorio antes de estudiar.

It is grammatically complete, idiomatic, and easy to understand.