"She eats" is not technically the same as "she is eating" - the latter is progressive - therefore they are translated into Italian differently ("lei mangia" / "lei sta mangiando"). Both "She eats" and "She is eating" both have the same French translation as French simply does not have a progressive tense or an equivalent.
Lei is she referring to a person we are talking about, in third person. The other case is different. I try to explain: If you want to refer in a formal way to a person you dont know, or a elderly, or your boss, etc..to someone you dont have confidence *usually a stranger, u use "Lei"., in place of "You", even if you are speaking directly to him/her. U need to think about those things, to spot the difference (Formal/informal)
I'm pretty sure it's conjugated equally or in the same manner. You just discern through context; once you are in the situation you will recognize so I wouldn't worry about that; I'd just instead keep in mind the nuance. Again, it's been over a month since I've even looked at my Italian flashcards, but I think it's the same with other romance languages that use the third person interchangebly with the first person singular formal.
Does anybody know of the credibility behind these people/robots (Whatever is used) for these pronunciations? I am just asking because I've went to google translate and pronunciations for some of these words (mangia in this case) seem to differ. For example, on google, the "G" is not pronounced like a G in "george" as someone pointed out above. Just wondering because it is rather difficult to want to learn when you are not sure if it will be wasteful in a real-life context.
Also, I went back to check what "Mangia" is pronounced like on google, and, I would not make a fuss about a difference in pronunciation as that could be do to regional differences, etc. but, the google one is "ManZa" Which, to me, at least, is a far cry from the G pronounced here.
I'm of Italian heritage in Brazil (doing the course to learn a bit more, since my parents speak very little of it). What I can say about the pronounces, from a bit of personal experience, is that Italian is composed of many dialects, and the pronunciation may vary from place to place. I already heard "mangia" like they pronounce here, I heard "manzia", like you said, and the dialect spoken where my grandparents came from pronounce it like "manha", like if it had that spanish 'n' (my tablet can't reproduce the letter, but I think you got the idea).