Tengo pensado estudiar español en la biblioteca este fin de semana.

It means something like I’m planning to..., I intend to..., or I’ve got it in mind to....

So:

Tengo pensado estudiar español
= I’m planning to study Spanish / I intend to study Spanish

It sounds a bit more like a formed intention than just a passing thought.

Because tengo pensado expresses a plan or intention, while estoy pensando usually means I am thinking about something right now.

Compare:

• Tengo pensado estudiar español este fin de semana.
  = I’m planning to study Spanish this weekend.

• Estoy pensando en estudiar español este fin de semana.
  = I’m thinking about studying Spanish this weekend.

The second one can sound less decided. The first one suggests the plan is more settled.

After tener pensado, Spanish commonly uses an infinitive to say what someone plans to do.

Structure:

tener pensado + infinitive

Examples:

• Tengo pensado salir temprano. = I’m planning to leave early.
• Tenemos pensado viajar en agosto. = We’re planning to travel in August.

So in your sentence:

Tengo pensado estudiar español...
the action being planned is estudiar.

Because this is a direct infinitive structure:

tener pensado + infinitive

Spanish does not need que here.

Correct:

• Tengo pensado estudiar español.

Not natural in this meaning:

• Tengo pensado que estudiar español...

If you want a clause with que, you usually need a different structure, such as:

• Pienso que... = I think that...
• He pensado que... = I have thought that...

But for I plan to do something, Spanish normally uses the infinitive.

Because after verbs like estudiar, names of school subjects and languages are often used without the article when speaking generally.

So:

• estudiar español
• aprender francés
• enseñar matemáticas

Using el can happen in some contexts, but in a basic sentence like this, español without an article is the most natural choice.

Because en la biblioteca tells you the location where the studying will happen: in/at the library.

• en = in / at
• a usually shows movement toward a place

Compare:

• Estudio en la biblioteca. = I study in the library.
• Voy a la biblioteca. = I’m going to the library.

In your sentence, the person is not focusing on going there, but on studying there.

In Spanish, time expressions like hoy, mañana, este fin de semana, este verano, and el lunes often appear without a preposition.

So:

• este fin de semana = this weekend
• mañana = tomorrow
• el martes = on Tuesday

English often uses on, but Spanish usually does not:

• Lo haré el lunes. = I’ll do it on Monday.
• Estudiaré este fin de semana. = I’ll study this weekend.

Yes, but the meaning changes a bit.

• este fin de semana = this weekend
• el fin de semana = on the weekend / at the weekend / during the weekend, depending on context

In your sentence, este fin de semana is specific: the upcoming or current weekend.

If you say:

• Estudio en la biblioteca el fin de semana

it can sound more general, like a habit, depending on context.

In this expression, tener pensado + infinitive is usually treated as a fixed structure, and pensado normally stays in the masculine singular form.

So both a man and a woman can say:

• Tengo pensado estudiar español.

This is very common and natural.

You may sometimes see agreement in other uses of pensado, especially when it clearly describes a noun:

• Tengo pensada una excursión. = I have an outing planned.

There, pensada agrees with excursión. But in tener pensado + infinitive, learners should usually treat pensado as fixed.

Yes. That is completely natural.

Pienso estudiar...
and
Tengo pensado estudiar...

both mean that you plan to do something.

The difference is slight:

• Pienso estudiar... = I plan/intend to study...
• Tengo pensado estudiar... = I’ve got it planned / I have it in mind to study...

Tengo pensado can sound a little more deliberate or pre-considered.

No, Spanish word order is fairly flexible, although some orders sound more neutral than others.

The original sentence is very natural:

• Tengo pensado estudiar español en la biblioteca este fin de semana.

You could also say:

• Este fin de semana tengo pensado estudiar español en la biblioteca.
• Tengo pensado estudiar español este fin de semana en la biblioteca.

These are all possible, but the position of the time phrase and place phrase can slightly change what is being emphasised.

The most neutral order is often: verb phrase + place + time which is what you have here.

It works perfectly in both Spain and Latin America.

Nothing in Tengo pensado estudiar español en la biblioteca este fin de semana is uniquely Spanish-from-Spain. It is standard, widely understood Spanish.

The only thing that can vary by region is style or preference:

• some speakers may prefer pienso estudiar
• others may use tengo pensado estudiar

But your sentence is natural across the Spanish-speaking world.

Yes, but the meaning shifts a little.

• estudiar español = to study Spanish
• aprender español = to learn Spanish

Estudiar focuses more on the activity or effort.
Aprender focuses more on the result.

So:

• Tengo pensado estudiar español... = I’m planning to study Spanish...
• Tengo pensado aprender español... = I’m planning to learn Spanish...

Both are correct, but estudiar fits better if you are talking about what you plan to do in the library that weekend.