Was there a school at the mission? if so, who attended its classes?

I have read in books that the Native Americans took "classes" after their morning work. I am confused because I thought there was a school at the mission that was only for Spanish. Was there a school at the mission? if so, who attended its classes?

While the neophytes were "instructed" there wasn’t a school or a dedicated group of teachers in the sense we think of this in modern terms. You are correct that the Spanish tried to teach the neophytes Spanish (with limited success) but most of the "instruction" they received was religious teaching or involved practical aspects of farming and mission operation. Neophytes selected to learn particular crafts (carpentry, candle making) received practical training as apprentices in those fields.

In 1815 the Spanish authorities prepared a List of Questions that had to be answered by the Fathers at each mission. Fr. Jose Senan (Father President) prepared an 18 page reply based on these local reports. Here are a few of the comments contained in this remarkable document:

• "The Indians here speak their own idiom. Some converse in
Spanish, but imperfectly."

• "The Indians…love their children but give them little or no
education. It is different at the Mission, however, where,
besides Religion, industry and agriculture is taught them."

• "[Some} neophytes, more out of curiosity than utility,
manifest some inclination to learn to read and write. With
charcoal, some of the boys at times draw characters on the
walls, as white boys do…"

• "There is no way of getting the Indians to devote
themselves more diligently to Spanish."

• "We have a catechism in the idiom of the Indians of the
Mission and also a catechism in Castilian. Instructions are
given in both languages alternatively."

• {the Indians] …" are ignorant of the calendar. Through their
language has distinct words for morning, noon, evening and
night, the pagans [unconverted Indians still living in their
villages], live to suit their fancy, do not understand anything
about this as far as eating, working and resting is concerned.
The neophytes [Indians living at the mission] are guided in
every thing by the Mission Bell."

• "They are now quite eager to sing and to play on the
instruments, string as well as wind, and they easily learn by
ear or by sight."