SHORT ANSWER:
The present perfect is used to describe an action which causes a present state.
The past perfect is used to describe an action which caused a past state.
LONG ANSWER:
The verb form usually employed to signify your started-and-finished in the past is the simple past.
I ate dinner.
This says nothing about what went before or came after. It is a complete 'historical' action, what grammarians call perfective (not 'perfect').
The perfect constructions in English signify something different. Although they name actions which occurred in the past, they define that past action as still relevant at a later time, as causing a state which endures into that later time.
The present perfect construction employs the present form of HAVE to signal that the later time is now, Speech Time, the time when you speak or write the sentence. You use this construction to describe your present state:
I have eaten dinner (so I'm not hungry now or so I can see you immediately without having to eat dinner first, or whatever the consequence is).
The past perfect construction employs the past form of HAVE to signal that the later time is then, Reference Time, the 'historical' time defined in the sentence's larger context by your use of simple past forms. You use this construction to describe your state at that time:
I had eaten dinner (so I wasn't hungry then).
Note that perfect constructions require a context. The context for using the present perfect construction need not be specified: it 'defaults' to the present, Speech Time. But you use the past perfect only when you are narrating past events: a Reference Time must be established by using one or more past forms.
Employing the present perfect makes a statement about Speech Time, the present.
Employing the past perfect makes a statement about Reference Time, a specific point in the past.
Note also that because the present perfect construction is a statement about the present, you are not permitted to use it with an adverbial referring to a point in the past:
✲ I have eaten dinner yesterday. This must be expressed as
I ate dinner yesterday.
✲ marks a usage as unacceptable
Let's look at a few more sentences in the same tense (present perfect) as your first example:
Mary has eaten the cake.
I have finished the report.
Someone has taken my phone.
In each case the first phrase of the sentence is the doer of the action (Mary does the eating, I do the finishing, someone does the taking.)
From this it is clear that your first example does not make sense (although it is grammatically correct). An idea cannot do the deleting. It does make sense, however, to say: Someone has deleted the idea (actually, deleted the file would be a better example).
Your second sentence, on the other hand, is both grammatical and makes sense. It is in the passive form of the same tense. If we convert the examples above to the passive, then we get:
The cake has been eaten (by Mary).
The report has been finished (by me).
My phone has been taken (by someone).
Your second sentence fits in here:
The file has been deleted (by somebody).
We use the passive like this when we want to shift the focus of the sentence away from the doer of the action. Maybe we don't know who did the action, or it is obvious, or we don't care who did it. The passive allows us to focus on what happened and does not require us to mention the doer.
Best Answer
It's probably pretty rare. I know I had to think pretty hard to come up with an example.
You can, however, use "There was..." instead of "There has been...":
Generally speaking, the difference is this: we use "has been" when something has just happened very recently (just moments ago, and we are just now reporting on it), whereas we use "was" when something happened much longer ago (like yesterday, or last week).
"There has had" sounds almost ungrammatical to me, except perhaps in examples where the word there happens to be adjacent to has had, for example:
although I suppose nearly anything can be made grammatical in the right context:
Yet even that sounds a little awkward, and there is a good chance I'd massage it before using it in an article.