Learn Russian: Какое поразительное совпадение!

Both are perfectly fine for exclamations! Какое acts as an adjective here and must agree in gender and number with the noun (neuter for совпадение). Что за is invariable and slightly more colloquial, so Что за поразительное совпадение! would also be entirely correct and natural.

Where does the word совпадение (coincidence) come from?

It comes from the verb совпадать / совпасть (to coincide). If you look at the roots, it's со- (together/with) + в (in/into) + падение (falling). So a coincidence is literally two things "falling into" place together!

Does поразительное translate literally to "striking"?

Yes! It comes from the perfective verb поразить, which means "to strike" or "to hit" (like hitting a target), and by extension "to astound" or "to amaze". Just like in English, a fact or event that is deeply amazing is described as "striking".

If I wanted to exclaim "It is the exact same coincidence!" using this lesson's topic, how would I do it?

Because совпадение is a neuter noun, you need the neuter forms of the exact identity pronouns. You would say Это то же самое совпадение! or Это одно и то же совпадение!