I used to be able to do some of those.....including the one armed and the handstand. Going from a head stand to a hand stand is a tough one too. Now with all my joints going bad I am reduced to girls style pushups.
Parallel dips are a close relative to pushups too, done on parallel bars....pullups too.
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[SIGPIC] Diesel loving autocrossing grandpa Architect. 08 Dodge 3/4 ton with Cummins & six speed; I have had about 35 benzes. I have a 39 Studebaker Coupe Express pickup in which I have had installed a 617 turbo and a five speed manual.

[SIGPIC]
..I also have a 427 Cobra replica with an aluminum chassis.