hi you could also try doing things like bench dips (you can use anything sturdy instead of a bench though ie end of bed, wall) these will strengthen your triceps so theyll help you with press ups ...
(you can try spider man press ups *text deleted*classic press up but as you lower your body bend your right leg and rotate your knee out until its outside your right elbow then repeat on other side*text deleted** )
also as said pull ups, you could do chin ups then for your core youve got sit ups, crunches, leg raises, plank, single leg lowering, side bridge..
hope that helps