Getting those push ups right

If there's anything that bothers me the most is not the burpees or squats, but the push ups. I do half push ups now(from my knees) but that's difficult too, I barely can touch the ground.

This is why I have given my core and arms better attention yet, if there's any progress, evidently, it has been ridiculously slow.

I enjoy russian twists and bridges and most other core workouts because I have seen myself get better at them but why not the same case with push-ups?

I have been here for 10 months now, on and off( BIG OFFS because I couldn't manage time) and I have seen myself get better at form, a tad bit of stamina and muscle strength.

Help me understand the science of push ups and figure out whether where I am is fine or what's going wrong, if it's not fine,

On the other hand, I am working on fitting all my activities and fitness into the 24hr time frame and that's going great!