There is a lot of code, so please ask if you require it. The video of the issue:
Impossible to give specific help without seeing the code.
Nonetheless using Time.deltaTime
and such accordingly is generally how things are made frame-rate independant.
Plenty of info in the manual: Unity - Manual: Managing time and frame rate
I solved it. Turned out that invoke is frame dependent (at least at 20 fps). So I redid it with booleans, timers and Time.deltaTime.