The first is correct for formal English but where I live you might hear the second often. I live in rural US South. Many people here especially the ones raised far from a big town.(7,000 in my case) will be more likely to us this form. Here is another example "to sell" something. I see and hear constantly "to sale" something. I see it written by people from all over my state The is used incorrectly. Everything else is ok she learned to cook and, other things about forest life.

Hello Tulay :) the first answer is correct as "learnt" is the past participle (3rd form) so you must use "has/have" or "had" before it (depending on which tense you are using). You can also say "She learned how to cook and to hunt" and this flows better. I hope this is helpful!

There are slight differences between British and American English. British English uses learnt and burnt. American English uses learned and burned. Source: Raymond Murphy, English Grammar in Use with answers 4th edition, Cambridge University Press, 2012, p. 301