El ordenador está encendido cuando estudio en mi cuarto.

Both mean computer, but they’re used in different regions:

• In Spain, the normal word is el ordenador.
• In most of Latin America, people say la computadora.

Since you’re learning Spanish from Spain, el ordenador is the natural choice here.

In Spanish, every noun has a grammatical gender that you just have to learn.

• Ordenador is masculine, so it takes el and masculine adjectives:
  
  • el ordenador encendido, un ordenador nuevo
• There’s no logical reason; it’s just the way the word has developed in the language.

The verb estar is used for temporary states or conditions. Here, being switched on is a temporary state:

• El ordenador está encendido. – The computer is on (right now / at that time).

Using ser (es encendido) would sound wrong in this context; it would suggest a permanent characteristic, which doesn’t fit. So for things like on/off, open/closed, clean/dirty you normally use estar in Spanish.

It looks like a past participle of encender (to switch on), but in this sentence it functions as an adjective describing the state of the computer:

• Verb: encender el ordenador – to switch on the computer
• Resulting state: el ordenador está encendido – the computer is on

So grammatically: estar + encendido = to be in the “on” state.

English uses on both for location and power state:

• The book is on the table.
• The computer is on.

Spanish separates these ideas:

• Location: en (in/on), sobre (on top of)
• Power state: encendido (switched on), apagado (switched off)

So for “The computer is on” (powered on), you must say El ordenador está encendido, not El ordenador está en or … está sobre.

The adjective encendido/encendida has to agree with the noun it describes:

• ordenador is masculine singular, so: encendido
• If the noun were feminine, e.g. la lámpara, you’d say: La lámpara está encendida.

So:
El ordenador está encendido. (masc. sing.)
Las luces están encendidas. (fem. plural)

Here, the idea is a habitual situation: whenever you study, the computer is on.

In Spanish:

• For general habits or repeated actions, use the simple present:
  
  • cuando estudio – when I study (whenever I study)
• The present continuous (estoy estudiando) focuses on what is happening right now.

So:

• El ordenador está encendido cuando estudio en mi cuarto.
  = The computer is on whenever I study in my room.
  If you said cuando estoy estudiando, it would sound more like talking about a specific ongoing situation.

Spanish verb endings already show the subject:

• estudio = I study
• estudias = you study
• estudia = he/she/it studies

Because estudio clearly means I study, the subject pronoun yo is usually omitted unless you want to emphasize it:

• Normal: Cuando estudio en mi cuarto…
• Emphasizing: Cuando yo estudio en mi cuarto… (e.g. contrasting with when someone else studies)

Yes, both word orders are natural in Spanish:

• El ordenador está encendido cuando estudio en mi cuarto.
• Cuando estudio en mi cuarto, el ordenador está encendido.

The meaning is the same. Starting with cuando… just gives a slightly different emphasis, but both are correct and common.

With possessive adjectives like mi, tu, su, nuestro, you do not use a definite article in front of them:

• mi cuarto – my room
• tu casa – your house
• nuestra escuela – our school

So en mi cuarto is correct.
en el mi cuarto is not standard Spanish and sounds wrong.

All can refer to a room, but there are nuances:

• cuarto – very common and general: room; in this context often understood as bedroom
• habitación – also room; a bit more neutral/formal; often used in hotels
• dormitorio – specifically bedroom (place where you sleep)

In everyday Spain Spanish, saying mi cuarto to mean my bedroom is very common and natural.

With cuando, Spanish uses:

• Indicative for habitual / repeated / factual actions:
  
  • Cuando estudio en mi cuarto, el ordenador está encendido.
    (Whenever I study in my room, the computer is on.)
• Subjunctive for future, not-yet-realized actions (often after a future reference):
  
  • Cuando estudie en mi cuarto, encenderé el ordenador.
    (When I study in my room [in the future], I’ll switch on the computer.)

Your sentence talks about a regular situation, so indicative (estudio) is correct.

You can, but the nuance changes slightly:

• cuando estudio en mi cuarto – when/whenever I study in my room
• mientras estudio en mi cuarto – while I am studying in my room

So:

• El ordenador está encendido cuando estudio en mi cuarto.
  Focus on the time or occasion.
• El ordenador está encendido mientras estudio en mi cuarto.
  Focus on the fact that the computer is on during the whole period you are studying.

Both are grammatically correct; choice depends on the nuance you want.