This 'ch' for c is 'Church' Latin. Rome was where the Churh as based and the pronunciation of Latin was influenced by Italian.
If the 'rule' is that C is 'ch' before ae, e, i, and oe, we should be pronouncing words derived from Latin as, for example, captive as 'chaptive' and Italians would be saying 'chapo' for 'capo';. and 'chapuccino'for'capuccino ! There is no such ruie in classical Latin and no word follows that scheme: Caesar, coelum (the sky or the heavens),Incitatus (the name of Emperor Caligula's horse;its name means 'gallops fast and' he made it consul ) cepit (he took, captured) are a few that come randomly to mind, and all have hard C.
V is U ? Well, yes, in that Latin text, notably in monumental inscriptions, often had U written as V. V itself is pronunced as W.