Okay, two questions:
1/ I have access to sets of 3lb, 5lb, and 10lb dumbbells; a 'balance ball'; and my own bodyweight.

What's the best way to make a decent at-home strength workout? Everything I've tried doesn't really feel like I'm doing anything, and I don't want to waste my time. I'm mostly concerned with upper body and core.
2/ This is kinda gross, but whenever I do pushups, when I go towards the floor my back fat/skin is pushed together (I guess...?) by my shoulder blades and it
hurts! Any way to change this, or should I just wait until I'm smaller to be doing pushups?