The basic difference between a past perfect tense and a present perfect tense is that the past perfect tense, as you have said is to tell us which event comes first when there are two past actions in the same sentence.
The present perfect on the other hand tells us about an event in the past that is relevant to the present. For example:
Look! I have found these two children who are lost.
The act of finding the children is relevant to the present because they are with you now and they are lost now.
this would not work becasue it isn't relevant to the present.2. The morning of the day I got sick, I have been thinking. (If this is not okay, why?)
Yes, it is something you did before you got sick and couldn't think anymore.