Help? I have been adopted by a stray chicken.

This girl(?) showed up a few weeks ago now, and i have asked around with my neighbors and also on the county FB group and no one seems to be missing a chicken. I have accepted that i just own a chicken now, but i would like some help with a few things.

1) what breed is she most likely?

2) any tips on identifying if its a hen or a roo? I have not found any eggs but its also just starting to warm up here and it hasnt had the best diet and i know both of those things contribute to egg production. She also could just be hiding them well. but that brings me to

3) what in the world do i feed this thing, I can't imagine living off of sunflower seeds and millet is the best for her.

and finally,

4)suggestions for a cheap shelter? shes been sleeping behind the ivy in my window well and we have a lot of racoons and possums around, so id like her to have a safe space, but i dont have a whole lot of income to build a whole coop and run, i actually have little to no income for it so, the cheaper the better.

ive been calling her Window Chicken and we have an uneasy alliance where she yells at me until i give her birdseed.