Learn Farsi: چه کسی کاشف این میکروب عجیب بود؟ - Who was the discoverer of this strange microbe?

To heavily emphasize the 'who', you can use the cleft structure you are learning: این چه کسی بود که این میکروب عجیب را کشف کرد؟ (Literally: 'Who was it that discovered this strange microbe?'). The sentence as written is a standard, non-cleft question, but it's the perfect prompt to practice a cleft answer, like: پاستور بود که این میکروب را کشف کرد (It was Pasteur who discovered this microbe).

Where exactly are the Ezafe links (the hidden 'e' sounds) in the phrase کاشف این میکروب عجیب?

There are two. The first connects 'discoverer' to the rest of the phrase: کاشفِ این (kâshef-e in). The second connects 'microbe' to its adjective: میکروبِ عجیب (mikrob-e ajib). Notice there is no Ezafe after این (this); demonstrative words like این and آن just sit directly in front of their noun. The full pronunciation is kâshef-e in mikrob-e ajib.

I know the verb for 'to discover' is کشف کردن (kashf kardan). How is کاشف (kâshef) related to it?

کاشف is the noun form meaning 'discoverer'. Because کشف (kashf) comes from Arabic, it can be put into the Arabic 'doer' pattern (inserting an 'â' sound after the first letter) to create کاشف (kâshef). You will see this pattern a lot in intermediate Farsi, just like ظالم (zâlem - oppressor) from ظلم (zolm - oppression).

Why does the sentence use چه کسی for 'who' instead of just (ki)?