Из‑за дождя мне не хочется выходить из дома.

Yes. Из-за is a fixed preposition, written with a hyphen.

In this sentence, it means because of or due to:

• из-за дождя = because of the rain

Be careful: из-за can also literally mean from behind, as in из-за угла = from behind the corner, but in your sentence it clearly has the causal meaning because of.

Because из-за requires the genitive case.

So:

• дождь = nominative
• дождя = genitive singular

That is why Russian says:

• из-за дождя = because of the rain

This is something you just have to learn with the preposition: из-за + genitive.

Because the construction with хочется uses the dative case for the person who experiences the feeling.

So:

• я = I
• мне = to me

Russian is not saying this in the same way English does. The structure is more like:

• To me, it is not felt/desirable to go out

Natural English becomes:

• I don’t feel like going out

So мне marks the experiencer, not a normal subject.

Не хочется means something like:

• I don’t feel like
• I’m not in the mood to
• I have no desire to

It comes from the verb хотеться, which is related to хотеть (to want), but it is more impersonal and often describes a feeling that just comes over you.

So:

• Я не хочу выходить = I don’t want to go out
• Мне не хочется выходить = I don’t feel like going out

The second one usually sounds softer and more about mood or inclination than a firm decision.

Because мне не хочется is an impersonal construction.

In English, we usually need a subject, so we say I don’t feel like.... But in Russian, some expressions work without a normal subject. Instead, the person involved appears in the dative:

• мне холодно = I’m cold
  literally: To me, it is cold
• мне скучно = I’m bored
• мне не хочется выходить = I don’t feel like going out

So the sentence is normal Russian even though there is no nominative я.

This is about aspect.

• выходить = imperfective
• выйти = perfective

With хочется, the imperfective often sounds more natural when talking about an activity in a general sense:

• не хочется выходить из дома = I don’t feel like going out / leaving the house

It presents the action as an activity or process, not as one single completed event.

If you used выйти, it would focus more on a single act of stepping out once:

• мне не хочется выйти из дома = I don’t feel like stepping out of the house

That is possible in some contexts, but выходить is very natural for a general reluctance to go out.

Here дома is genitive singular of дом because the preposition из requires the genitive.

So:

• дом = house/home
• из дома = out of the house / from home

This can be confusing because дома can also be an adverb meaning at home.

Compare:

• Я дома. = I’m at home.
• Я выхожу из дома. = I’m going out of the house / leaving home.

In your sentence, after из, it is definitely the noun дом in the genitive case.

They are doing two different jobs:

• из-за = a fixed preposition meaning because of
• из = a separate preposition meaning out of / from

So the sentence breaks down like this:

• Из-за дождя = because of the rain
• выходить из дома = to go out of the house / leave home

Even though both contain из, they are not the same grammatical unit here.

Yes. Russian word order is fairly flexible.

Your sentence:

• Из-за дождя мне не хочется выходить из дома.

is perfectly natural and emphasizes the reason early: Because of the rain...

You could also say:

• Мне из-за дождя не хочется выходить из дома.

That version puts мне first and may sound slightly more centered on your feeling.

The basic meaning stays the same. Word order in Russian often changes emphasis more than core meaning.

A rough literal breakdown would be:

• Из-за дождя = because of the rain
• мне = to me
• не хочется = it is not desired / I don’t feel like
• выходить из дома = going out of the house / leaving home

So, very literally:

• Because of the rain, to me it doesn’t feel desirable to go out of the house.

That is not good English, but it helps show how the Russian grammar works. The natural translation is:

• Because of the rain, I don’t feel like going out.