First, "I am yet to do my homework" is not correct. One would still say, "I have yet to do my homework." Second, you may use the phrase "have yet to," but it will always sound more formal. I hear it often on a television show called "Downton Abbey." It takes place in England around 1910 to 1920, and the aristocrats speak very proper English. Perhaps it is still used more commonly in Great Britain; I don't know. I'm from the U.S., and we would not say it that way very often. Examples: "I have yet to see a stupid person" = "I haven't seen a stupid person." (The first sentence isn't the best English, so the second is also poor. What is really meant is "I have yet to meet a stupid person," and the updated version would then be, "I haven't met a stupid person.") "I have yet to do my homework" = "I haven't done my homework (yet)." "I have yet to go to England" = "I haven't gone to England." (This is also an odd example. We would prefer to say, "I haven't been to England" when we flip the sentence.) The full understanding of most sentences, of course, is only known through context. In the homework example above, since the anticipation is that you still must do your homework, it is acceptable and even preferred to use "yet" again at the end of the sentence. The other two sentences rely on your intent. If your sociology professor gives you an assignment to go out and find stupid people specifically and ask them questions, and if you've been trying for hours to find one, you might say, "I haven't met (or found or seen or talked to) a stupid person yet." The "yet" implies that you have been trying to accomplish the task, but it is still ongoing. However, if some loudmouth at a party comments that "People in general are stupid," you might respond, "Really? I haven't met a stupid person. All people have something to offer." No "yet" is needed because you aren't in an ongoing search for a stupid person.

The explanation is wrong. Present perfect does not refer to actions started but unfinished. That would be the present continuous. The present perfect refers to time frames that have started but haven't finished. What happens, or doesn't happen, within this time frame is said in the present perfect. I have yet to go to England. The time frame here is "ever", or probably the persons life time. It could also be his summer holidays, which aren't over yet. In either case, he hasn't been to England yet within this time-frame. yet to go = he hasn't even started out on his journey there If he has already started out on his journey to England, he would say: "I have yet to arrive there."

I can see that you are a very diligent student, but actually you're overanalyzing this. "Have yet to X" and "be yet to X" have exactly the same meaning, and they both mean "haven't X yet." I agree with Gena that "have yet to" is probably more common, but "be yet to" is also something we sometimes say in American English.

In America we would not use "I am yet to do my homework." I guess the meaning is "I am supposed to do my homework". We would say "I still have to do my homework...I haven't done it yet." "I have yet to go to England" implies that he has not even started going to England yet. If he were on his way, he would say "I have not arrived in England yet, but I'm on my way.