There is an excellent book called "primitive photography", aother one with te title "experiments with pinhole and self-made caeras" or similar.
Not only pinhole, but also other cameras can be made at home with little effort: rewarding are, for instance, hyperfocal cameras - can be done with simple lenses!
Eggs without dichromate does not sound promising to me. Of course they dry and rot in daylight, but that is about it. Dichromate is just poor-man enough, and will give first-rate quality at prices considerably lower than normal photographic paper.
For exposure, there is always the sun.
And cyanotype is always pretty economical, too.