I have concerns that your joints are not stong from what you posted, problems in your elbows doing planks and wrists doing push-ups. If you have done weights with machines before your muscle strenght could exceed your joints ability to use this stength in body weight excersises and lifting real things that arn't stabilized for you.
Bodyweight excerises should solve this over time if it is the case, and if you really need to do low rep stuff get something unstable like a sandbag, or maybe a lamb, they get heavier as they grow and you can eat them when they get big.
You know all those pictures of Adam and Eve where they have belly button? Think about it..................... take as long as you need........................