El comedor está lleno a mediodía, así que las profesoras ayudan a las niñas a encontrar sitio.

Because lleno describes a temporary or changeable state here: the dining hall is full at midday, not permanently full.

In Spanish, estar is commonly used for states or conditions:

• El comedor está lleno. = The dining hall is full.
• La puerta está abierta. = The door is open.

Using ser here would sound unnatural, because it would suggest being full is a defining characteristic of the dining hall.

Here, comedor means dining hall or cafeteria, especially in a school context.

Although comedor can also mean dining room in a house, in this sentence the school setting suggested by las profesoras and las niñas makes dining hall/cafeteria the most likely meaning.

Both can exist, but a mediodía is a very common way to say at midday / at lunchtime.

• a mediodía = at midday
• al mediodía = around midday / at midday

In many contexts they are very close in meaning. In this sentence, a mediodía works as a time expression meaning at lunchtime / at noon.

Así que means so, therefore, or so that’s why.

It introduces a consequence:

• El comedor está lleno a mediodía, así que...
  = The dining hall is full at midday, so...

It is very common in everyday Spanish for linking cause and result.

Because the sentence is specifically referring to female teachers and girls.

• las profesoras = the female teachers
• las niñas = the girls

If the group were all male, or mixed in traditional grammar, you would normally see:

• los profesores
• los niños

So this is not a grammar rule being applied randomly; it is telling you who the people are.

That a is required because las niñas is the indirect object of ayudar in this structure.

With ayudar a alguien, Spanish normally uses a before the person:

• Ayudo a mi hermano.
• Ayudan a las niñas.

This is not exactly the same as the so-called personal a used with direct objects, because ayudar is conventionally built with a before the person it helps.

Because the structure is:

ayudar a alguien a hacer algo
= to help someone do something

So:

• ayudan a las niñas = they help the girls
• a encontrar sitio = to find a place/seat

Put together:

• ayudan a las niñas a encontrar sitio
  = they help the girls find a place

That second a introduces the infinitive phrase.

Because encontrar sitio is a very natural expression meaning to find space, to find room, or to find a seat/place.

Spanish often omits the article in this kind of general expression:

• No hay sitio. = There’s no room.
• Buscamos sitio. = We’re looking for a place/space.
• Encontrar sitio = to find somewhere to sit / to find room

If you said encontrar un sitio, that would also be possible, but it can sound slightly more specific: find a place. Without the article, it feels more general and idiomatic here.

It can suggest all of those, depending on context.

In this sentence, because the dining hall is full, encontrar sitio most naturally means:

• find a place to sit
• find room
• find a seat

In Spain, sitio is very commonly used this way in everyday speech.

Lleno is an adjective, so it agrees in gender and number with the noun it describes.

Here:

• el comedor = masculine singular
• so: lleno = masculine singular

Compare:

• El comedor está lleno.
• La sala está llena.
• Los comedores están llenos.
• Las salas están llenas.

Because Spanish normally leaves subject pronouns out when they are not needed.

The verb form ayudan already tells you it is they help. The noun phrase las profesoras also clearly gives the subject.

So Spanish prefers:

• las profesoras ayudan...

rather than:

• ellas ayudan...

A subject pronoun would only be added for emphasis, contrast, or clarity.

Sometimes, yes, but not always with exactly the same nuance.

• profesora = teacher; often used quite broadly, especially in schools
• maestra = primary school teacher, or teacher in a more traditional sense

In many contexts they may overlap, but profesoras is a very normal choice here. In a school setting in Spain, it sounds natural.

Not necessarily. In real usage, it can mean:

• at noon
• around midday
• sometimes even at lunchtime, depending on context

In this sentence, since it is about a dining hall being full, the idea is probably closer to at lunchtime / around midday, not necessarily the exact clock time of 12:00.