Pushups -- try Diamond Pushups. Bring your hands closer to each other so your thumbs and forefingers form a diamond.
Squats -- try a variation that puts most (or all) of your weight on one leg. For example, do a lunge, but before rising up, lift your rear foot off the floor.
Core -- when you are on the bar doing pullups, do some leg raises (lifting your legs so they are straight in front of you). If that is too tough, bend your legs to a degree that makes them more doable.