They both just take practice.
For push-ups, the gap between on-the-knees push-ups and on-the-toes push-ups seems rather wide. Instead, try doing straight-leg push-ups with the front body elevated. Beginners would start with hands on a wall. Then, as one progresses, go to hands on a kitchen counter. Then to the rim of a bathtub or the seat of a kitchen chair. Then to a step set at 12". Then 10", etc.
For pull-ups, there are several methods:
1) assisted pull-ups/chin-ups (chin ups--with palms facing you--are a bit easier, because the biceps help more): put a kitchen chair (weighted down with barbell plates) in front of the pull-up bar, where you can rest your feet on it, and a stool under the pull-up bar (tall enough so you can reach the bar without jumping when you stand on it. Stand on the stool, then put your feet on the back of the chair. Pull yourself up, using your legs for help. Play with the distance of the chair: you might need to move it closer to get more help from it. Gradually reduce the amount of 'help' it gives you (by having it farther away so you can't push against it as much, and/or by using just one foot to push).
You can also do assisted chin-ups/pull-ups using bands or using an assisted pull-up machine in a gym.
2) negative chin-ups/pull-ups: use the same stool/bar set-up, but no chair involved. Propell yourself off the stool to get above the bar, hold for 2 counts, then lower as slowly as you can.
3)don't know what to call these:
Put a body bar across two kitchen chairs, or use a ballet bar, or put sturdy dowel across the bottom of a staircase (if there are handrails on both sides, and something to keep the dowel from rolling---I have a hard time explaining this one!). Lie on the floor under the bar, and pull yourself up. To start with, you may need more assistance, so bend your legs (and reduce the amount of wt. your back has to pull). As you progress, straighten your legs, then go to one leg.
You could even combine more than 1 of these methods: do assisted chin-ups for as many reps as you can, then do a few negative chin-ups.
HTH