From what I've heard, the fine for overstaying is so low ($25 to $50) that it's not worth bothering extending the 90-day tourist visa. But an extension can be done.

For learning Spanish, I've just been doing duolingo and of course daily use, always attempting to speak and understand in Spanish (I pick up languages somewhat quickly and speak fluent French, which is similar to Spanish), though there are also local teachers for doing one-on-one and surely some classes.