Start with negatives. If you belong to a gym with a fixed chin-up bar, stand under the bar, and then jump up and grab it, using momentum to help pull your body to the top position
You are encouraged to take those days off, as they will help you maximize your gains from the program. Here’s the reason: In order for you to build strength, power, and athleticism
Given your current fitness level and joint issue, I’d start with PiYo. It’s a beginner to intermediate level program that will be easy on your joints while helping you burn fat and build mobility and strength
If bench/chair dips hurt your shoulders, swap them for the triceps push-up.
Sounds like you’ve established a strong fitness foundation, and I applaud your desire to build on it. I hesitate to recommend individual workouts from specific programs, because they aren’t designed to work that way. Our programs are designed so that each workout builds on the one before