I have all the respect in the world for practitioner's of Western martial studies so the following questions are posed to help people get to the right sources:
The bigger question and I am not saying this to begin an argument or be rude is are there "real" experts on medieval fighting?
Depends on what you mean by "real" (beyond your following exposition). If you mean people using the same weapons with repeatable, verifiable, results in fighting which look like the available historic images and match the available historic texts, then, "yes."
Meaning, if most of the information we have has been translated from manuscripts do they really understand what people did back then?
That's the $64,000 question, isn't it? It's sort of the same question that Flint Knappers get asked. "Are you sure that's how the cavemen did it?" The answer is, naturally, "We can't be 100% sure but I take the same inputs and get the same outputs so if it ain't exactly the same, it's pretty darn close." This is additionally bolstered by the fact that the human body hasn't changed at all since then. It still breaks in the same way and moves in the same ways. There's only going to be so many ways to make a given tool "work" against a human.
If there are "experts" who are they? How did they become and expert in their system?
<shrug> Look around. Find people who's stuff works against other people in resisting confrontations. Ask them how they got where they are.
The other major question is what lineages do we have that have been passed down for generations and did not need to be reinvented or revived from a manuscript?
As we've seen many times, having an unbroken "living lineage" doesn't necessarily prevent changes in the system. Crap, Ueshiba died in 1969 and how many different styles of Aikido are there? You'd think that Nikyo would be the same in all of the, but it isn't. They're usually pretty similar but not always identical. I used to believe that having an unbroken lineage would ensure the veracity and purity of an art. Now I'm not so sure.
But, anyway, on to the question. The answer is, "yes, there are unbroken instructor lineages." However, the answer is also, "no, the transmission of certain weapons is 'broken'." Most research into the subject seems to indicate that the people who were instructing "back then" taught others who then went on to instruct and pass their lineage on to the next generation instructor. However, what weapon(s) they were teaching fluctuated and evolved with whatever the common and/or in-demand weapons of the time were. This is most obvious in the German tradition where we see an evolution of Medeival "knightly" weapons taught and then, as they fell out of vogue, were slowly relegated to more and more sporting or "historic" interest weapons, which gave way to more "modern" weapons. For example, Joachim Meyer's fighting manual shows what was in his time "antique" Longsword (apparently for basic instruction and sport), "modern" Dussak (saber-like weapon), and emerging Rapier. Crucially, he says that all of the weapons are unified under the same method and system of body movement. In other words, the "rules" for how to use all of these very different weapons are the same at their basic level, merely modified in order to be most appropriate for that given weapon.
These same Fencing schools continued on right up to today, where I could easily go study Smallsword or Foil with a direct lineage descendant from antiquity. But Smallsword isn't Longsword. Not by a long shot. However, because we know that these schools evolved from there, because we have a living instructor for the modern "rules" of movement and use, because we have texts describing the "rules" of movement and use for the "dead" weapon systems, then, yeah, I'd venture that a pretty close approximation is possible and, perhaps, identical interpretations are possible to achieve even if impossible to "prove." The "rules" for "verification" really haven't changed: Does it match the extant descriptions and images? Does it work? Does it follow the "rules" of fencing theory, particularly any listed in the manuals?
If you are training in the US or Europe where and who would be a good person to study with? Why?
Big places.
Peace favor your sword,
Kirk