Should I do push-ups every single day?
Five days a week is the sweet spot for most people. Daily works if every set stays well short of failure, but the moment you start grinding reps, you need the rest days back.
Do knee push-ups count?
They build something, but they change the movement enough that progress transfers poorly. Incline push-ups against a table or a wall are the better regression — same shape, less weight.
My wrists hurt.
Try push-ups on your fists or on dumbbell handles so your wrists stay straight. Muscle soreness in your chest and triceps is expected; sharp joint pain in the wrist or shoulder means change the setup rather than push through.
Is 20 push-ups actually a good benchmark?
It's an arbitrary round number, but it's a genuinely useful one. Twenty clean reps means real pressing strength and a torso that holds a line, and it makes most other upper-body work easier.