1.“This mountain has never been climbed by anyone. Several mountaineers have tried to reach the top, but nobody has ever succeeded. The climb is extremely difficult and many people have died trying to reach the summit.”
Why is present perfect used in that sentence?
Because we are talking about the situation so far - this text is about what has happened in the period up until now. Nobody has climbed the mountain yet, but one day someone probably will. The time period 'until now' is unfinished or 'open', so we use the present perfect.
2.“Our parents bought this painting at an auction about 55 years ago.” Instead of “our parents have bought…”.
'55 years ago' is a finished time period. With finished or 'closed' time periods, you have to use a past tense. You can never use a present perfect form with 'ago'.
3.“They say that somebody invented the wheel by chance.” Instead of “somebody has invented…”.
The wheel was invented a long, long time ago. It would be very strange to say that 'somebody has invented the wheel' as if it were news! We would say, for example 'Guess what I've just heard? Somebody has invented a cure for cancer!', because this is news of something which has just happened.
I hope that helps.