How do I parse the Zhou Enlai quote 为了中华之崛起而读书?
You parsed the sentence correctly, and got the correct meaning for most of them.

之 means 的 (of). And 而 is a conjunction, to connect the two subsentences. It's not necessary but if you want you can take its meaning as and / and then / and yet ... to help understanding.

PS: The google translation is quite straightforward and correct.