There are no grammatical mistakes here. The punctuation is not very good though. Secondly, YOU have typed this out very badly. Seriously, if you want us to help you need to take much more care in presenting your stuff. All in all, the sentence is too long, with too many conjunctions. Add a few full stops here and there and it will all become clearer.

Your teacher is a woman, she needs to get some logic chip implanted to be a very good teacher. You are too, so be sure.) And her tongue may be is not English. Mine is not either, but what sounds out of place is, (rewritten a bit) ..........later conquered the land later known as California, ....... after getting (don't know the whole story) independence, and it returned ( who?, be specific here)

This sentence is too long and badly constructed with incorrect use of partciples (fighting). It would be better to write.'In the 16th century Spanish soldiers arrived in South America, where they fought against the natives and took their land. Two centuries later they ruled California, which became part of Mexico after the independence of Mexico from Spain in 1821. California was returned to the USA after the war which the USA declared on Mexico.