Mi hermana da la vuelta al filete con una espátula de madera.

Because dar la vuelta a algo is a very common Spanish expression. In this sentence, it means to turn something over / flip it. Spanish often uses a verb + noun expression where English prefers a single verb.

In cooking, dar la vuelta a sounds very natural in Spain.

Because the expression is dar la vuelta a algo. That a is part of the structure.

So you start with:

da la vuelta a el filete

But in Spanish, a + el always contracts to al:

a el → al

So the correct form is:

da la vuelta al filete

Yes. That is also very common.

Both of these are natural:

• Mi hermana da la vuelta al filete
• Mi hermana le da la vuelta al filete

That le is a very common extra pronoun with this kind of structure. It does not change the basic meaning here. In everyday Spanish, especially spoken Spanish, many speakers like to include it.

Sometimes, but they are not always the best match.

• dar la vuelta a = very natural for turning something over, especially in cooking
• girar = more like to rotate / turn around
• voltear = understood, but in Spain it is generally less common than dar la vuelta a in this kind of context

So for Spain Spanish, dar la vuelta al filete is a very idiomatic choice.

Con is the normal preposition for the tool or instrument used to do something. So con una espátula means using a spatula / with a spatula.

The article una is there because it means a spatula, not a specific previously mentioned spatula.

Because de madera describes the material something is made of: wooden or made of wood.

In Spanish, material is often expressed with:

de + material

So:

• una espátula de madera = a wooden spatula
• una mesa de metal = a metal table
• una cuchara de plástico = a plastic spoon

You normally do not use the article here, so de la madera would sound wrong in this sentence.

Because in modern standard Spanish, possessive adjectives like mi, tu, su, nuestro usually come without an article before the noun.

So you say:

• mi hermana
• tu casa
• su coche

Not:

• la mi hermana

Also, notice that mi here has no accent. That is different from mí, which is a pronoun meaning me after a preposition.

Da is the present tense of dar for ella:

• yo doy
• tú das
• él/ella da

The present tense in Spanish can be used in several ways, depending on context:

• for something happening now
• for a habitual action
• for recipe/demo-style instructions

So this sentence could describe what she is doing right now, or a normal action in a cooking context.

It can move. The original order is very natural and neutral:

Mi hermana da la vuelta al filete con una espátula de madera.

But Spanish is flexible, so you could also say:

Con una espátula de madera, mi hermana da la vuelta al filete.

That version puts more focus on the tool. The original sentence is just the most straightforward word order.

You know from the articles:

• al filete = a + el filete, so filete is masculine
• una espátula = feminine

With people, gender often matches real gender, as in hermana. But with objects like filete and espátula, you usually have to learn the noun together with its article:

• el filete
• la espátula

That is the safest habit.

No. It is a very common expression with several meanings depending on context.

For example, it can mean things like:

• turn something over
• turn around
• go around
• come back / return in some contexts

Here, because the object is el filete and the tool is una espátula, the cooking meaning is clear: to turn it over / flip it.