La puerta de vidrio del balcón deja entrar mucha luz.

Because de + el contracts to del in Spanish.

So:

• de el balcón → del balcón

This contraction is required in normal Spanish, except when El is part of a proper name, such as de El Escorial.

Here, del balcón means of the balcony or, more naturally in English, to the balcony / balcony’s depending on context.

In Spanish, the material something is made of is very often expressed with de + noun.

So:

• puerta de vidrio = door made of glass
• mesa de madera = wooden table
• caja de metal = metal box

English often uses a noun as if it were an adjective, but Spanish usually does not do that in the same way. So de vidrio is the normal structure.

Both are correct, but in Spain, cristal is often very common when talking about panes, windows, or glass doors.

So a Spanish speaker in Spain might also say:

• La puerta de cristal del balcón...

That can sound especially natural for a door with glass panels or a sliding glass door.
Still, vidrio is completely correct and clearly understood.

A rough idea is:

• vidrio = glass as a material
• cristal = often used in everyday speech for window/door glass

But in real usage, there is overlap.

It most naturally describes puerta.

So the structure is:

• La puerta
• de vidrio = made of glass
• del balcón = the balcony door / the door to the balcony

In other words, this means something like:

• the glass balcony door
• the glass door to the balcony

Spanish often stacks these de phrases after the noun, so you have to read them carefully.

Here the most natural interpretation is that it is the balcony door, and that door is made of glass.

Because dejar + infinitive is a very common Spanish structure meaning:

• to let
• to allow
• to make it possible for something to happen

So:

• deja entrar mucha luz = lets a lot of light in

Literally, deja entrar is something like lets enter, but in natural English we would usually say lets in or allows ... to come in.

This structure is very common:

• La ventana deja pasar el aire.
• Esa abertura deja entrar el sol.

Also, the subject does not have to be a person. An object can dejar entrar something too.

Yes, absolutely. In fact, dejar pasar mucha luz is very common and very natural.

Compare:

• deja entrar mucha luz = lets a lot of light come in
• deja pasar mucha luz = lets a lot of light pass through

Both work well here. The difference is small:

• entrar focuses on coming in
• pasar focuses on passing through

With light, air, and sound, dejar pasar is especially common.

Yes, that is grammatically correct too.

Compare:

• deja entrar mucha luz
• deja que entre mucha luz

The first version is more compact and very common with dejar + infinitive.

The second uses a subordinate clause with the subjunctive:

• que entre

Why subjunctive? Because after dejar que, Spanish normally uses the subjunctive to express what is being allowed.

Both are correct, but deja entrar mucha luz often feels simpler and more direct in this kind of sentence.

Because luz here means light in a general, uncountable sense.

So:

• mucha luz = a lot of light

If you say luces, that usually means lights as separate things, like lamps, bulbs, or light sources.

For example:

• Hay mucha luz en la habitación. = There is a lot of light in the room.
• Hay muchas luces en la habitación. = There are many lights in the room.

Also notice:

• luz is feminine
• so it takes mucha, not mucho

Because grammatical gender in Spanish is not determined only by the ending. While many feminine nouns end in -a, plenty do not.

Luz is simply a feminine noun:

• la luz
• mucha luz

This is something learners often just have to memorize noun by noun.

Other common feminine nouns that do not end in -a include:

• la imagen
• la flor
• la noche

Because after de to express material, Spanish usually does not use an article.

So:

• de vidrio
• de madera
• de plástico
• de metal

This is the normal pattern when you mean made of that material.

You would add an article only if you were talking about a more specific noun phrase, for example:

• de un vidrio especial
• del vidrio reciclado

But in the basic material sense, de vidrio is exactly what you would expect.

Because the subject is La puerta, which is singular.

The rest of the phrase:

• de vidrio
• del balcón

just gives more information about puerta. It does not change the number of the subject.

So:

• La puerta ... deja = singular subject, singular verb

If the subject were plural, the verb would change:

• Las puertas de vidrio del balcón dejan entrar mucha luz.

It could be changed, but it may sound more ambiguous.

• La puerta de vidrio del balcón clearly suggests the glass door of/to the balcony
• La puerta del balcón de vidrio could make the listener momentarily wonder whether the balcony is the thing made of glass

Spanish often relies on word order to reduce ambiguity in strings of de phrases. So the original order is helpful and natural.

If you wanted to be even clearer, you could also say something like:

• La puerta de vidrio que da al balcón...

But the original sentence is perfectly good Spanish.