I wish to ask about the impact of human effort. What is the proportion of human effort and God's will on overall scheme of things? In other words, can human effort change or impact what is destined to happen?
If you have the penance, then to some extent, you can change the fate. Otherwise, there is absolutely no free will.
Do we have the choice to control a desire? I mean, is it destiny (prarabhdha) that controls a desire or is it a personal choice?
Swami Vivekananda says, ‘If you are because of what you did in the past, then your future is what you are now!’ So, yes, desires can be controlled.
How can we differentiate our will and Divine will?
If your ego decides, then it is your will. Otherwise, it is divine will.
You have told that "Where there is faith there is no fate" as well as "There is no free will at all". Are they both not contradicting? If there is no free will, is one attaining liberation also pre-determined?
The only will we have is the freeing will of choosing to chant whenever we find mind wandering. So there is no free will, but only a freeing will of chanting the Mahamantra with faith in its power.
So liberation cannot be attained by any amount of will power, but purely by the grace of a Guru or God. So chant and the debate of free will versus destiny will get resolved by itself.