Once you've done one there's no stopping.
G told me those don't count...
If by half you mean with one arm then yes they do count.
I think I want to see video of these pushup lessons with Biddy. This way I can learn some stuff too!!
Knee push-ups definitely count in my opinion! Good stepping stone.
It really depends on what you are doing push ups for. If for "core" then toes are more "productive". If for shoulders then knee position can be very effective as it keeps (or should do) shoulders over hands and delivering the correct downward movement. Often we slide "backwards". As someone who shouldn't do pushups on toes (foot stress fracture) I'm now using a plinth as support for just above the ankle so almost a toes pushup.
"what you are doing push ups for"
To please Biddy :)
I use toes and just alter the height of what I'm pushing from depending on how strong I'm feeling...