Try ladder sets like 10-9-8-7-6-5-4-3-2-1 or EMOM like 10 minutes every minute you do for example 5-6 reps and over time u will get more reps

@Lucas Lim Increase pull up Volume and frequently doing your pull ups Do 2-3 times in week pull ups Do also weighted pull ups, ladder sets, EMOMs

It would be beneficial to train the Handstand before starting with planche training, because the free HS teach you alot for planche training and also like Planche Presses or Planche Negatives are good exercise for Planche and if u cant hold a handstand good than it could be a problem in the future

Concentrate on free Handstanding attempts, dont stay to much at the wall. Learn to bail out and learn to dont fear fails to fully concentrate on the balance. Try handstands everyday to get better at that balance skill its important to gain much time in a handstand. And when doing on the floor concentrate on gripping the floor with your fingers. When you got more questions feel free to ask bro

Usually not. Try to warm up your shoulders and chest more before doing dips. Watch some videos about the technique and work on it. Dont lean too much forward, that will put much more stress on your shoulders