We are a commune of inquiring, skeptical, politically centrist, capitalist, anglophile, traditionalist New England Yankee humans, humanoids, and animals with many interests beyond and above politics. Each of us has had a high-school education (or GED), but all had ADD so didn't pay attention very well, especially the dogs. Each one of us does "try my best to be just like I am," and none of us enjoys working for others, including for Maggie, from whom we receive neither a nickel nor a dime. Freedom from nags, cranks, government, do-gooders, control-freaks and idiots is all that we ask for.
I would recommend it as an excellent first-thing-in-the-morning daily light warm-up/workout for beginners. Since no HIIT or weights (only hand-weights) are involved, no recovery is needed so you can do either weights or HIIT cardio on the same day with no problem.
Remember that calisthenics like these are for athleticism, light cardio, and general fitness maintenance. There is no strength gain or cardio gain involved, but that is not what it is for. I did feel great after doing it. If you are new to the fitness cult, I'd recommend this as a daily morning routine before advancing your program too much further.
Yes, I would advise first thing in the morning, right after slugging down a quick cup of coffee and before opening your computer. Unlike an hour of heavy calisthenics, this will leave you pumped up for the day instead of ready for a nap.
I didn't do the 100 pushup challenge but I have been trying to do a cals routine every weekday morning - 100 abs (20 each crunches, leg lefts, in-n-outs, left and right side jacks), 50 bodyweight squats, and working up to 50 pushups (sets of 10 squats/pushups between each abs). So far doing pretty well. Can finish in about 10 minutes with a light sweat. As I get more comfortable I'm going to add more sets .. two count crunches, swimmers, etc.