Learn Farsi: این اختراع یک انقلاب بزرگ در علم بود. - This invention was a great revolution in science.

While اختراع (ekhterâ') means 'invention' (creating something entirely new), کشف (kashf) or اکتشاف (ekteshâf) means 'discovery' (finding something that already existed, like a new element or planet). Since the sentence talks about a human-made creation, اختراع is the correct choice here.

Where does the Ezafe sit in the phrase یک انقلاب بزرگ در علم?

It links the noun to its adjective: enghelâb-e bozorg. There is no Ezafe after بزرگ because the preposition در (in) naturally breaks the Ezafe chain. It is a common mistake for learners to add an Ezafe before a preposition, but you should simply pause slightly: yek enghelâb-e bozorg [pause] dar elm.

Instead of using the word یک (yek), could we use the indefinite suffix ـی (i) on the noun phrase?

Yes! You could say انقلابِ بزرگی (enghelâb-e bozorgi). Both mean 'a great revolution'. In everyday spoken Farsi, it is also very common to combine both for emphasis: یه انقلابِ بزرگی (ye enghelâb-e bozorgi).

If this invention affected multiple branches of science, what is the plural form of علم?

In academic or formal contexts, Farsi heavily uses the Arabic 'broken plural' (an irregular plural formed by changing the word's internal vowel structure) for this word: علوم (olum), meaning 'sciences'. For example, علوم کامپیوتر is the standard way to say 'computer science'. While the regular Farsi plural (elm-hâ) is understood, is the term you will almost always encounter.