There may be differences in AmE and BrE, especially with have got. I am answering as generically as I can.
I've got this video game
can be a special case. There is an idiomatic usage of have got as a present tense verb. As such it is equivalent to have.
We've got lots of time to talk.
and
We have lots of time to talk.
mean the same thing. And the verb combination have got is used as a present tense verb. As I said, this is a unique case.
However "have got" (or: "have gotten" in AmE) can be used as present perfect. Thus, you can compare
I've just got/gotten this video game
with
I just got this video game.
In these two sentences, the meaning is very close. So close that one could say that in this case, the simple past and the present perfect have the same meaning. In both sentences, the time period referred to is the recent indefinite past (recently in the past). This is because of the adverb just. Other adverbs that have this effect include: already, recently, still, yet.
I think that BrE speakers prefer the present perfect here, while speakers of AmE can just as easily use the simple past.
As for the first pair of sentences.
Did you ever go to China?
and
Have you ever been to China?
First, it is correct to recognize that the present perfect have been to a certain place is equivalent to
Have you ever gone to (and returned from) China?
And again, there is no great difference in meaning between the simple past and the present perfect. Both refer to a time in the indefinite past. This is due to the use of the adverb ever.
However, if you get rid of the adverb ever, the simple past and present perfect have different meanings:
Did you go to China?
This question is referring to a specific time in the past. Perhaps the speaker mentioned that she planned to go to China at a specific time, and now someone wants to know if indeed the speaker went at that specific time. The speaker is referring to the whole event of go to China as an event that began and ended in the past and does not include the moment of speaking.
Have you gone to China?
The speaker is referring to an indefinite past time period that he believes has psychological relevance at the moment of speaking. Such as: I am asking you if you have gone to China at some/any point in the past and implying that such a past trip must now be relevant to you, in some such way as the past experience makes up part of you you are as an individual now.
However, if you name a specific time in the past, the present perfect is not usually used:
Did you go to China last summer?
is fine. But
Have you been to China last summer?
will not be judged as grammatical by all native speakers. Many will point out this construction conflicts with the basic meaning of the present perfect as referring to an indeterminate past event with current relevance at the moment of speaking. Some speakers will not use the present perfect when referring to a specific time in the past.
The following would probably be judged as ungrammatical by all native speakers:
*Has Germany won the World Cup on June 16, 2014?
whereas
Did Germany win the World Cup on June 16, 2014?
is fine.
There are many cases when the present perfect simply cannot be replaced by the simple past and mean the same, which is the point of your question:
I have read this book from 9pm to 10pm.
Although the start and end times are mentioned, the use of the present perfect refers to an indefinite past time, and thus this means that the reading could have started earlier than 9pm and/or ended later than 10pm.
However
I read this book from 9pm to 10pm.
strongly indicates that the specific period starting at 9pm and ending at 10pm is meant, and that period only. Whatever the case, the use of the simple past is used to report an event that started and ended in the past and does not include the present.
Also consider:
I have studied English for 12 years.
The implication is that the speaker is still studying English at the moment of speaking.
I studied English for 12 years.
The use of the simple past refers to past time only. It does not include present time. The speaker is referring to an event that began and ended in the past. The statement says nothing as to whether the speaker is studying English at the moment of speaking. The implication is that he is not.
There are other answers about the difference between simple past and present perfect that you can read if you search for "present perfect" and sort by either relevance or recent.