At least two approaches offer themselves to this question.
The first is to produce a list of one right to know after another. We list our intuitions or what there is a broad consensus about in our society. Your examples fit this approach. Much may be said for it. Against it is the danger that we finish up with a disconnected heap of rights to know without any unifying theoretical basis. This is perhaps all we can get, so my observations so far are not presented dismissively.
But let's try, which I think you want, to see if a more systematic list can be delivered.
1.I have a right to know that p if you have a duty to give me the corresponding information, which you possess accidentally. We stand in no particular relationship but you happen to know something you have a duty to tell me. You may by chance, for instance, have discovered that I am radically misinformed about a matter of vital concern to me, e.g. my imminent betrayal by a business partner whom I trust.
2.I have a right to know that p if someone with a special obligation to tell me the truth knows that p. If my consultant knows that I have prostate cancer, then I have a right to know that p from this special-relationship person.
3.I have a right to know that p if not knowing that p significantly reduces the lifeplan options and alternatives available me.
What unites these cases is that they all involve, if in different ways, my interests - a workable but not crystal-clear and unambiguous concept. A missing factor is 'who has the obligation to fulfill my right to know that p?' In one case there is no special relationship with the person who has the duty to tell; in another, there is precisely such a relationship; and in the last there is no obvious agent whose duty it is to fulfil my right to know unless we invoke the ultimate pseudo-agent of 'society'.
This answer is tentative and incomplete. I would do better if I could. Most likely others will supply my defects.