Learn Finnish: Se kysyy päivityksestä. - He is asking about the update.

In Finnish, verbs related to thinking, talking, or asking (cognitive verbs) often require the elative case (-sta/-stä) to express what the action is about. Because kysyä (to ask) is one of these verbs, 'about the update' becomes päivityksestä.

How exactly does the word päivitys change into päivityksestä?

Päivitys (update) belongs to a group of words ending in -us/-ys. When adding a case ending to these words, the final -s changes to -kse- to form the grammatical stem. So, päivitys becomes the stem päivitykse-, and then you add the elative ending -stä.

The English translation says 'He', but doesn't se mean 'it'?

Yes, in standard written Finnish, se means 'it' and hän means 'he' or 'she'. However, in everyday spoken Finnish, native speakers almost exclusively use se to refer to people. This sentence reflects how Finns actually speak.

Would it be wrong to write päivityksesta instead?

Yes, that would break the rules of vowel harmony. The root word päivitys contains the front vowels ä and y. Because of this, any endings attached to it must also use front vowels, which is why it takes -stä instead of the back vowel equivalent -sta.