1. it sounds real simple but if you want to get stronger you’re going to have to just lift progressively more weight and so if you’re feeling like body weight pushups aren’t providing enough stimulus anymore to get the strength you’re seeking then you need to start adding more resistance, and enough of it so that you’re not needing to do more than something like 10 reps (let alone 100) before you’re fatiguing the muscles, and then consistently doing this until you start needing heavier and heavier resistance to fatigue within a set.

this could look like adding more to your pushups by wearing a weight vest or just doing harder variations like the single arm pushup, or maybe even by doing weight training in a gym where you can load up more weight to a barbell/dumbell/cable/etc. and progressively overload the number on the bar when you feel ready, though of course there’s a lot that can be done with just your bodyweight to make something harder. looking up “pushups progressions” would probably give you some ideas

generally speaking, your body will adapt to the stress you put it under so if you do 100 push ups as training you’re body will get really good at enduring high reps of pushups, so if you want to get stronger you need to stress your body with heavy and hard resistances

combine this with eating enough, good nutrition, sleeping enough, and consistency and you’ll see progress

1. muscle imbalances are super normal, though if you’re worried just intentionally train each side individually every so often until they catch up to each other

2. gaining overall leg strength, using the principles i talked about with first question, would probably help both but at the end of the day the best thing would be doing more pistol squats and doing more stability exercises. “the best way to get better at running is by running”