Cuando el cielo se pone gris, prefiero quedarme en casa.

Because cuando here is a conjunction meaning when.

• cuando = when
• cuándo = when? in a question or indirect question

Examples:

• Cuando llueve, me quedo en casa. = When it rains, I stay home.
• ¿Cuándo llueve más en tu ciudad? = When does it rain more in your city?

So in Cuando el cielo se pone gris..., there is no question, so it is cuando without an accent mark.

Ponerse often means to become or to turn when talking about a change of state, especially a temporary or visible one.

So:

• el cielo se pone gris = the sky turns grey / becomes grey

This is a very common use of ponerse:

• ponerse triste = to become sad
• ponerse nervioso = to get nervous
• ponerse rojo = to turn red

In this sentence, se pone gris sounds natural because the sky is changing appearance.

It is pronominal: the verb is normally used as ponerse in this meaning.

A beginner may think it literally means the sky puts itself grey, but that is not how Spanish speakers understand it. It is just the normal verb form for become / turn in this context.

So you should learn ponerse + adjective as a pattern:

• Me pongo cansado.
• Se pone oscuro.
• El cielo se pone gris.

Because gris is an adjective that does not change for gender in the singular.

• el cielo gris
• la nube gris

In the plural, it does change:

• los cielos grises
• las nubes grises

So in this sentence, gris agrees correctly with el cielo.

Spanish often omits subject pronouns because the verb ending already shows who the subject is.

• prefiero = I prefer

So yo is not necessary unless you want emphasis or contrast:

• Yo prefiero quedarme en casa, pero ella prefiere salir.

Without emphasis, prefiero alone is perfectly natural.

Because after preferir, Spanish normally uses an infinitive when the subject stays the same.

• Prefiero quedarme en casa. = I prefer to stay at home.

Structure:

• prefiero = I prefer
• quedarme = to stay / to remain

The me is attached to the infinitive:

• quedar + me = quedarme

You could also say:

• Prefiero salir.
• Prefiero descansar.
• Prefiero quedarme.

But Prefiero me quedo en casa is not correct.

Quedarse means to stay, to remain, or to stay behind.

So:

• quedarme en casa = to stay at home

This is a very common expression in Spanish.

Compare:

• Voy a casa. = I’m going home.
• Estoy en casa. = I’m at home.
• Me quedo en casa. = I’m staying at home.

In this sentence, quedarme gives the idea of remaining at home instead of going out.

Because en casa is the usual idiomatic way to say at home.

• Estoy en casa. = I’m at home.
• Prefiero quedarme en casa. = I prefer to stay at home.

If you say en la casa, it usually sounds more like in the house/building, focusing on the physical place rather than the idea of home.

So:

• en casa = at home
• en la casa = in the house

Both verbs are in the present indicative:

• se pone = present
• prefiero = present

This present tense is often used for habitual actions or general situations:

• Cuando el cielo se pone gris, prefiero quedarme en casa. = Whenever the sky turns grey, I prefer to stay at home.

It does not have to mean only right now. It can express a repeated preference or a general truth.

Yes, cuando can be followed by either the indicative or the subjunctive, depending on the meaning.

Here it uses the indicative because it refers to something habitual, general, or seen as real:

• Cuando el cielo se pone gris, prefiero quedarme en casa. = Whenever the sky turns grey, I prefer to stay home.

If you were talking about a future event that has not happened yet, Spanish often uses the subjunctive:

• Cuando el cielo se ponga gris, me iré a casa. = When the sky turns grey, I’ll go home.

So:

• cuando + indicative = repeated / usual / factual
• cuando + subjunctive = future or not-yet-realized event

Because the sentence begins with a subordinate time clause:

• Cuando el cielo se pone gris, ...

When this kind of clause comes first, a comma is commonly used to separate it from the main clause:

• Cuando tengo tiempo, leo.
• Si llueve, no salgo.

If the time clause comes after the main clause, the comma is usually omitted:

• Prefiero quedarme en casa cuando el cielo se pone gris.

So the comma here is natural and helps mark the structure clearly.

Yes, but the meaning is slightly different.

• se pone gris = turns grey / becomes grey
• está gris = is grey

So:

• Cuando el cielo se pone gris... focuses on the change
• Cuando el cielo está gris... focuses on the state

Both can be correct, but se pone gris is especially good if you want the idea that the sky starts to look grey.

Because Spanish normally talks about the sky as a singular noun, just like English does here.

• el cielo = the sky

If you made it plural, it would usually change the meaning or sound poetic/literary:

• los cielos

In ordinary everyday speech, el cielo is the normal choice.

Yes. You can also say:

• Prefiero quedarme en casa cuando el cielo se pone gris.

The meaning is basically the same.

Starting with Cuando el cielo se pone gris puts the condition/time context first. It sets the scene before giving the main idea.

Starting with Prefiero quedarme en casa puts the focus first on your preference.

Both are natural.

Yes. Preferir is a stem-changing verb.

Its infinitive is:

• preferir = to prefer

In the present tense, the e in the stem changes to ie in most forms:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos prefieren

So prefiero is irregular in exactly the way learners often expect from verbs like querer or pensar.

Sometimes, but they are not exactly the same.

• estar en casa = to be at home
• quedarse en casa = to stay at home

Quedarse suggests remaining there, often instead of leaving or going out.

So:

• Prefiero estar en casa = I prefer being at home
• Prefiero quedarme en casa = I prefer to stay at home

In your sentence, quedarme en casa sounds more natural because it expresses a choice about what to do when the weather changes.