"yet" is more common using it with a present or future tense. I am eating lunch, yet I am not hungry. I have yet to purchase the tickets. I have not found my briefcase yet.

Only with the present perfect although you may hear some people use it with the simple past but that would be incorrect and informal. It's best to only use it with the present or past perfect. Hope that helps.

Do you have an example in mind? Different tenses can be used with the word yet depending upon the meaning. They have yet to meet. (They still haven't met each other.) They lived in the same city but had not yet met. (At a point in the past they they didn't know each other but have subsequently met each other.) They may yet meet. (It is possible that they will meet in the future.)

You're welcome!!