It's easier to do a hand stand and then balance against a wall. I can't for the life of me do a real handstand.
Is there any advantage of the archer pushups over just doing one arm pushups?
Well, that sounds like a pretty good warm up to me.
its not easy for you there is a barrage of info, most coming from the same place, some just silly
the basic principal of strengh training is adaption by progressive over load, progressive over load is easy in a gym you just put more weight on, with body weight you need to try a bit harder, by juggling volume(how much weight you lift in total or number of reps) and intensity, how heavy it is, or how hard you make it if your doing fast or slow.
but the principal with push ups, would be to start light, by leaning on a counter and do lots of volume to get the muscle working and start the adaptation process, then as you get better, come down in height(which increases the intensity) but do lower reps.work your way down in volume and up in intensity. Till you are doing proper push ups at say 10 reps and build to do say 5 sets of these.
then the problem is that as you are just doing the same exercises over again, the strengh gains,stop.
so you need to make it harder again, so you can elivate your feet, go very fast or very slow or do one of the many push up variations' like archer push up or diamond push ups.
you want to make it difficult enough that you cant get above say 20 reps and when you can dp an easy 20 make it more difficult so you are back to 5or 8 again.
that way to are specifically developing strengh rather than endurance
nb archer push ups are a good bit easier than one armed push ups, not just on the arms, but particularly on the core muscles, that need to be very strong to stop you tipping over