"The Naked Warrior" can be your guide
Doing 100 pushups doesn't mean you are very strong at all. First you will have to start with higher-intensity pushups.
Try doing ones with your legs elevated to make them harder.
Along with those, start doing one handers where you make the movement easier, such as leaning against a kitchen counter to give you more leverage.
Gradually add tougher moves until you can start doing one-handed negatives(come down as slow as possible).
Then in time you will be able to do a one hander
For the balance part, just make sure to tense up your entire body, especially at your abdomen
Start with doing the elevated-feet puhsups and also bring your hands closer to work the triceps more. These should be quite challenging