I believe there's a problem with your terminology...
when you say "merge" -- we think of combining two different profiles into a single profile. This can't be undone, but can be fixed by recreating.
but it sounds like you actually mean, "connecting" relationships to your branch of the tree (father, mother, children, siblings, spouse, etc.)
and when you say "delete" -- we think you mean to completely erase the existence of... (which we don't allow, except under very special circumstances)
In order to "delete"/remove a mistaken connected relationship, go to the Edit tab of one of the affected profiles. On the right side, there are several links for add/remove father, mother, children, spouse, etc. Click the link and follow the steps (which may involve scrolling all the way to the bottom of the next page)