Hi... wow.. that's a big change. Sounds like a fun adventure.
Rents for a one bdroom in that area will be between $600 to $1000. Check out the information on this page, which includes links to popular online real estate sites. You will also find realtors who will help you. https://www.expatperu.com/renting-an-ap ... lima-peru/
Regarding the hair, etc.... out of my depth, but I can tell you that there is an afro-peruvian population here which have many of the same needs, so the products must exist.