Interestingly, Vocative form in Czech sometimes has an "-e" ending, like Petr - Petře (common first name) or profesor - profesore (professor)
I am getting a mixed message here: are initial h characters pronounced or not? With some recordings, with "habeo," it was. Here it is not. I feel the silent h would be more appropriate in modern times given other Romance languages, but older Vulgar Latin had the h pronounced originally, so which are we using here?
Yes, /h/ is supposed to be pronounced if you want a Classical pronunciation.
Currently Duolingo isn't using any real pronunciation because they tried to use Classical pronunciation and failed.
It is interesting, I speak Spanish (native),some Portuguese and Italian and none of them have these vocative thing and they are Romance languages. I do know there is something like this in Slavic languages such as Serbian
In modern times, Romance languages do not have cases even they originated from Latin. Slavic languages, on the other hand, do. Serbo-Croatian's got 7 of them (ablativus is divided into two new cases), while Russian's got a bit more if I'm not mistaken.