I'm not home yet. I haven't been home. yet = not now but I'm going there An no, it is not compulsory.

No. Your first example implies that you aren't at home but will be soon. If you just said "I am not at home," then you aren't implying anything about whether you will be there soon or not. It's just a statement. The same thing applies to your second sentence. "I haven't been at home yet." implies that you plan to be there, whereas "I haven't been at home" just states that you haven't been there recently.

In the second sentence in your example, the use of the present perfect is acceptable. However, the sentence would read, ''I haven't been home yet." You would use the present perfect in the following instance. Let's say one day your wife said she had to go out of town and asked you to clean the house that day. While you were still at work she phoned you and asked if you had cleaned the house yet. You would say, "No, I haven't done it because I haven't been home yet." (Notice, we would not use "at" in this sentence.)