Do followers of Jansen (I note Jansenist is fairly politically incorrect since it was coined by the Pope to attack followers of Jansen) believe in double predistination like Calvinists, or only in irresistable grace? Or is there perhaps a conflict among Jansen's followers?
I just don't know enough about Jansenism to say, I'm afraid. I will say, though, that I personally cannot see a difference between double predestination and irresistible grace. If God has the ability to ensure that some people are, irresistibly, saved, and if he uses this ability at all, then he's deciding which people will be saved and which won't. Which as far as I can tell simply is double predestination. A world in which irresistible grace exists but double predestination is not true seems to me to be inconsistent.
AFAIK, Panentheism is belief that god is the universe yet at the same time is more. This is what makes it distinct from pantheism. But maybe I missed a point.
The problem is, people define these things differently. Some people who identify as pantheists define "pantheism" precisely as you've just defined "panentheism". Both seem to me to assert that there is nothing that isn't divine, which seems to me to be the essence of pantheism, whether one thinks that there's more to the divine than just the physical universe or not.
Their sources could have invented it. It could be a confused mishmash of events, which, upon being collected into one volume, was written down by the Gospels. Roman records, Jewish Messianism, anything could have contributed. So while it may be possible that Jesus existed, the fact that the Gospels don't appear to have invented him isn't proof that he existed.
Once you start speculating like this anything goes. You can't
prove that Jesus existed any more than you can
prove that almost anyone else in history existed, but it's a question of what's reasonable. If you rule out deliberate fraud on the part of the authors of the only sources we've got, what's the point of speculating about other kinds of fraud on the part of hypothetical sources that we haven't got?
Of course there was Jewish Messianism at the time, but that's reason for thinking that charismatic figures might be hailed as the Messiah when in fact they weren't. And indeed there are a number of examples of this kind of thing happening in the first century. But this isn't a reason for thinking that such a person was completely made up. I don't know of any examples like that. As for "Roman records", I don't know what you mean by that. What sort of records? How would the Christians have got their hands on them? How could such records have formed the basis for inventing a person altogether?
It seems to me, as a rule, that folk memory is capable of embellishing the truth about people, and often quite dramatically and quite quickly. But it's far less easy to invent a person altogether, at least not nearly so quickly. Obviously there are examples of widely-believed-in people who probably didn't really exist, such as King Arthur, who was generally accepted as a historical figure in the late Middle Ages and early Renaissance (Henry VII called his eldest son "Arthur" in a deliberate attempt to legitimise his own house). But (a) even there it's possible that Arthur really was originally a real person, just about, and (b) much more importantly, this was many centuries later. Something similar might be said about Ossian, the supposed author of the epic cycle "collected" by James MacPherson in the eighteenth century (he actually wrote it himself on the basis of some oral traditions); in reality there was no Ossian. But here again there was a huge gulf of time between the supposed historical figure and the present, and there were no details given of his life, only his supposed authorship of certain texts.
Are there any examples of cases like Christianity and the Gospels, where a lot of specific information is given about somebody who lived just a few decades earlier and where that person did not in fact exist at all? I can't think of any.
The fact is that the historical sources, and the standards of proof applied to them by scholars, in the case of Jesus are comparable to those associated with many other characters from antiquity and indeed the Middle Ages, yet no-one seriously doubts the existence of (say) Socrates, Honi the Circle Drawer, or St Francis of Assisi. Only because it's Jesus do people insist on stronger proof and invent speculations about how he
might be fictional. The onus is on them to explain why Jesus should be treated differently from other historical figures in requiring such stronger evidence.