Present Tense – ‘Got’ vs. ‘Have Got’

The Cambridge History of the English Language, Vol 6, confirming what Barrie England wrote in his answer, says:

In tracing the history of American grammar, it is important to note that in many instances what might seem to have been a change in American English compared with the standard English of Great Britain is in fact no change at all - it is British English that has changed, not American. For example, eighteenth-century speakers of English generally formed the past participle of get 'receive' as gotten, as in Your brother has gotten my mail. In the nineteenth century, prestigious speakers in England began to drop the -en ending: Your brother has got my mail. Most Americans, however, continued using the older form gotten.

1 and 2 are both correct, and at least from US usage probably occurs relatively equally. However, the impression is not quite the same.

1. Kristina has passed her exam!

This implies that it was unexpected, or that she had some difficulty passing her exam.

1. Kristina passed her exam!

This is just a simple statement of fact (other than the !).

a. She has got 90%.

You can't use "got" with a helper verb. Should be "has gotten".
But I think "has gotten" is a poor word to use in this context. Something like

Her score was 90%.

is probably better.