This project brings back memories. I worked somewhere over 20 years ago where we were working on something just like this (touch displays using cameras). The biggest challenge was definitely the lighting conditions as you mentioned. We tried to rely on natural light but it was too unreliable. Darker skin tones were harder to pick up, and then you had issues with random reflections, light and shadow being cast on the screen, etc., which would make the system detect spurious fingers and touches.

We also had algorithms to detect finger shape to detect location of the pointer and when you were touching the screen. I saw way too many videos of fingers touching screens back then, so it's funny to see similar video clips here.