Have you taken a look at/heard of “Convict Conditioning?” Some good bodyweight progressions in there. Not sure what your goal is but below are some ideas.
Assuming you are strong enough, handstand pushups against a wall are a good exercise (where you are facing away from the wall, easiest way is to do a headstand next to a wall and do pushups from that position).
Also, do parallel bar dips, if you don’t have parallel bars somewhere then improvise (I’ve done them in the corner of an L-shaped kitchen counter before).
Lower body is a bit harder, as when I used to do bodyweight exercises I could not challenge my legs hard enough to make them grow without weight. You could add things like doing 10 broad jumps in a row or other explosive exercises. Hill Sprints are good too (sprint up the hill, walk down, repeat).
By the way, for an easier one-arm pushup, space your legs farther apart and on the way down, bend your torso away from your arm.
If I were you though, I would at the very least find a way to invest in some cheap/used dumbbells. It will be harder to progress in strength/muscle without weights.