You're right, we havent -ae- or -oe- but their sound it's the modern italian "e". About the hard "C", we have it, as you say, in -ca-, -co-, -cu- but also in chi- and che-.
About the latin -ti (like in DIVITIAE") became -zi-, a sound that i think doesnt exist in english. Every italian, if he learns this, can read latin, even a child.
PS
I study latin (let's say i'm forced to study it about 2-3 hours in a day), french and english. But i study them only from few years, so, please, forgive me if i make grammar mistakes.
If i say you how old i am, you could be surprise i know a language like latin