this exercises look very good. how many times in a week would you recommend doing this?
It really depends on other things you do.
As I mentioned, in Summer I didnt have a gym, which means I didn't have any exercises devoted to back, shoulder and I could barely do pullups with the bar so basically all of my upperbody was free to do push-ups every day, so I did it 3 or 4 days a week but never on consecutive days... That push-up workout as a whole, if done complete and right, is really hard, and even today, I couldn't repeat it with the same quaility if I tried to do it in two consecutive days.
if you go for them, don't mind doing longer pauses between exercises, specially the jump burpees, they WILL mess up your heart rate so take your time.
the difficulty level varies a lot from exercise to exercise, in me personal experience this is how I feel about them:
Very Hard:
Jump Burpees (breath right or fail by the 10th or so repetition)
Swinging Leg (flexibility of a martial artist or a dancer, all while doing pushups? yeah...)
Hard:
Scorpion
Spider
Moderate:
Triforce
Alternate Grip Single Leg
Easy:
Basic
Elevated
so it would be wise to try all of them, see how you personally rate their difficulty and then mix them so that you have different difficulties throughout the whole workout and not get exhausted too fast by doing the hard stuff in one part.
I currently mix those pushups with machines from the gym but that's a bit more than enough, so once a week is enough for me now. Besides, if you can do other bodyparts the rest of the week is better, I think.
but everyone must reach their own conclusions regarding frequency, load of work, reps, sets, etc.. but do try them and see for yourself, they are fun