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.
Sometimes, not only in English but in all languages, we want to emphasize certain situations. And then the language itself gives us devices that aren't always common, but we use them anyways, based on known and meaningful expressions.
I am very hungry
We can depict that the subject has surpassed the status of just "hungry" for they must have stayed a long time without eating. This is a known meaningful expression.
Murder is very illegal
From this, even if it doesn't make much sense in the binary nature of the word "legal", we can depict that "murder" is a crime that, morally or ethically, has surpassed the status of "illegal".
We can state that by looking at another not-so-serious crime:
Parking on the sidewalk is illegal
Yeah, we all know it is illegal and wrong. But it is a petty crime compared to murder. In some countries murder is penalized with life imprisonment, even with death penalty, while parking on the sidewalk gives you a fine and, in the worst of the cases, your car is towed.
We can still say that "Murder is illegal", of course it is, but in the sentence, the "very illegal" was made to emphasize.
Best Answer
Without any other context, (b) is the best option. "The atmosphere has been proved to extend several hundred kilometers above the Earth" does the best job of providing the necessary context within the sentence.
"The atmosphere proves to extend several hundred kilometers above the Earth" would sound better if it were preceded by a statement like "When measured using radio-scattering technology".
"The atmosphere is proved to extend several hundred kilometers above the Earth" would sound better if it were preceded by a statement like "In the work of Professor Braun".