He salido de casa sin paraguas.

In He salido, he is the first-person singular form of the verb haber in the present tense:

• yo he = I have
• tú has = you have
• él/ella ha = he/she has

So He salido literally means I have gone out / I have left.

This he has nothing to do with the English pronoun he.

Both are possible, but they are used a bit differently.

• He salido = present perfect
• Salí = preterite/simple past

In Spain, the present perfect is very commonly used for actions connected to the present time period, especially today or very recently.

So:

• He salido de casa sin paraguas often suggests something like I’ve left home without an umbrella / I left home without an umbrella, with relevance to now.
• Salí de casa sin paraguas sounds more like a completed past event, more detached from the present.

This is one of the classic differences between Spanish in Spain and many Latin American varieties, where salí is often used in situations where Spain Spanish prefers he salido.

Salido is the past participle of salir, which means to go out, to leave, or to come out, depending on context.

Forms:

• infinitive: salir
• past participle: salido

So:

• he salido = I have gone out / I have left

In Spanish, casa often appears without an article when it means home in a general, personal sense.

Very common expressions:

• estar en casa = to be at home
• ir a casa = to go home
• volver a casa = to return home
• salir de casa = to leave home

So de casa here means from home or from the house/home in a natural idiomatic way.

If you say de la casa, it sounds more like you are referring to a specific physical house/building, not simply home as the normal place where you live.

After sin (without), Spanish often leaves out the indefinite article when speaking generally.

So:

• sin paraguas = without an umbrella
• sin dinero = without money
• sin problemas = without problems

Sin un paraguas is possible, but it sounds more specific or emphatic, as if you want to stress not even one umbrella or a particular umbrella.

In an ordinary sentence, sin paraguas is the most natural choice.

Salir de casa is a very common expression meaning:

• to leave home
• to go out from home
• to leave the house

It is a normal collocation in Spanish. Learners should think of salir de as a common pattern:

• salir de casa = leave home
• salir del trabajo = leave work
• salir de la oficina = leave the office

No. In standard Spanish, h is silent.

So he is pronounced roughly like eh.

That means:

• he salido sounds like eh sa-LEE-do

This is true for almost all words with h in Spanish:

• hola
• hotel
• haber
• hecho

The h is written, but not pronounced.

Yes, Spanish word order is flexible, but some orders sound more natural than others.

The most natural version here is:

• He salido de casa sin paraguas

That keeps salir de casa together as a familiar unit.

You could also hear:

• He salido sin paraguas de casa

This is grammatically possible, but it sounds a bit less neutral. It may place slightly more attention on sin paraguas.

So for a learner, He salido de casa sin paraguas is the safest and most natural order.

Here it is best understood as home.

Although casa can mean both house and home, in expressions like:

• estar en casa
• volver a casa
• salir de casa

it usually has the sense of home.

So He salido de casa sin paraguas is naturally understood as I left home without an umbrella.

Because salir by itself already means to go out / to leave.

• He salido de casa = I have left home / I have gone out from home

The reflexive form salirse exists, but it usually has a different nuance, depending on context, such as:

• leaving unexpectedly
• going off course
• coming out accidentally
• overflowing
• stepping outside a limit

So in this sentence, plain salir is the correct and natural verb.

Paraguas is normally masculine:

• el paraguas
• un paraguas

Even though it ends in -as, it is masculine. That can surprise learners.

Also, paraguas usually has the same form in singular and plural:

• el paraguas = the umbrella
• los paraguas = the umbrellas

In your sentence, there is no article, so you just see:

• sin paraguas

But if you added one, it would normally be:

• sin un paraguas