"Have yet to" and "have not yet" have similar meaning. The main difference is in how they are used in sentences. "Have yet to" means that there is something, such as an activity, task or event, which has not occurred or which has not been done yet. For example: I have yet to finish my homework. This sentence means that you want to finish your homework but you have not finished it yet. "Have not yet to" is grammatically incorrect. "Have not yet" is correct, which means that there is some activity, task or event, which has not started yet. For example: I have not yet begun to do my homework. This sentence means that you want to do your homework but have not started doing it yet. I hope the difference is clear to you now. =)

"Have yet to" implies that you still have to do something. "Have not yet" implies that you still have not done something. If you substitute "still" for yet it makes it easier to understand the nuances. I have yet to do my homework. I still have to do my homework. I have not yet done my homework. I still haven't done my homework. The first implies that you plan on doing your homework in the future, the second only tells us that in the current situation, you have not done your homework, regardless of your future plans. To be honest though, now and days the phrases are pretty interchangeable.

"have not yet to" doesn't exist as an expression.