Problem! Questions are necessary to be able to help, so please give an answer to each.
#1. How old is the male chinchilla you have now?
#2. Where did you get this information?
I have decided to go with a young female because it is said that opposite sexes of chinchillas tend to get along better.
#3. When you say a "young female", how old a female are you thinking about getting?
#4. How much do you know about breeding chinchillas?
The basement would be nice, if it is a finished basement, because it is quiet, but
scheduled play times and scheduled visits need to be set and kept ... chinchillas love a routine and need to know they have not been abandoned.
You can use a "natural sunlight" bulb or a grow bulb in a lamp in the basement for 7 hours a day and there should be enough "sunlight" for your chinchilla.
The main concerns about using the basement are moisture and "two small windows", not so much for the sunlight needed, but for ventelation.
Chinchillas need fresh air.Will check back later for your answers.
Jo Ann