Yes you actually can build muscle with calisthenics - and GAIN WEIGHT TOO! So - these exercises require rest for you to truly grow ESPECIALLY at the volume you are doing each day. At 500 / 500 / 100+ reps a day, you should only do that every other day MAX.

Is it OK to do push-ups and pull-ups together?

Working both push and pull exercises helps to prevent injuries and avoid overtraining because you are differentiating between muscle groups and movement patterns. By incorporating both pushups and pull-ups into your workouts, you are allowing your body to work both motions.

Can you build muscle with just pushups and pullups?

A Weighty Matter

If your goal is to build muscle, push-ups and pull-ups will definitely add to your muscle mass if you do enough of them. ... With body weight exercises like push-ups and pull-ups, you might add weight by wearing a weight vest or ankle weights, but you're still more or less tethered to whatever you weigh.