@Aldis So a smart person (or a family) can create their own language as long as that language has meaning for the user then the magic should work though I think symbols would be the most effective form of language to use considering they are faster to write.
maybe each magic family has their own coded language, with how some of the students assume the MC use the family language I assume Noble families would have their own language system to be use in magic, or advance mages are advice to make their own codes they are probably just teaching the basics that's why they are using a common language for teaching.
now the way how mages battle works assuming they don't know the meaning of the language their opponents is then a mage with great memory and learning skill would have the advantage considering just seeing the spell a few times could make you learn the word their writing and understand it's meaning by looking at the effect. so yeah faster writing speed could counter it considering they have to see you write it first . predicting could also be a factor cause intention is a lot more important than the word itself so if you can predict you opponents intent then you can hijack their magic.
the magic system is quite interesting tbh you can probably create a battle manga out of this and it would be sprinkled with language facts, I have only seen one manga that talks about language and it's about a guy moving to an island full of monsters trying to learn their language accompanied by a loli wolf girl.