«ora» means "now," except when accompanied by an article as in «l'ora» (making it evident that it is a noun in such a context), where it means "hour." In the expressions «Che ora è?» or «Che ore sono?», «ora»/«ore» still mean "hour"/"hours" respectively; they could literally be translated as «What hour is it?» and «What hours are they?». The only thing is that, in English, we do not say that, and both expressions would be more idiomatically and correctly translated as "What time is it?". Now, «tempo» means "time," except for when it means "weather," which is perfectly distinguishable in context.
Hope this helps.
One question for italians natives ¿do you pronunce "non ho" as "no no" in a normal conversation? I've been thinking about that this days, because is a kind of annoying make the pause between "non" and "ho". But is not just with "non ho" is the same with "non" + hai, ha.
Carlos, I am not a native Italian, but I've been taught that the O in "ho" is an open O, compared to the closed O in non and no, so "non ho" should sound different than "no no", even with no pause between the words. The example given was "l'ho" vs. "lo".
Another Italian vowel with two sounds is E, for seven vowels sounds in total. Easier than English vowels, maybe?