This answer may be a little specific to one part of the question, so apologies if it's not suitable as a top level comment. It also address the Fisher King as literary / mythical figure rather than a historical one.

The Fisher King was a mythical figure in Grail romances (as far as I know, there is no historical personage to which the name is attached), the first of which was Chretien de Troyes' Perceval (1181 - 1190, unfinished). He's a somewhat cryptic figure in de Troyes' romance, a crippled nobleman who is lord of the Grail Castle. Briefly, Perceval finds the castle at the start of the romance, sees the bleeding lance and Grail paraded before him; as he fails to ask as to the nature of the Grail though, the castle is abandoned in the morning, and he is left to search for the Grail Castle. He finds it again, but again he fails to live up to expectations, and so must go questing again until he meets the Fisher King again, whereupon he is deemed worthy and bequeathed the Grail.

In de Troyes' romance, there are all kinds of allusions and metaphors going on around the Fisher King. The Fisher King is so named because he received a wound from a javelin "through his thighs." Since this has left him crippled and unable to enjoy the usual noble pleasures, he is lifted into a boat and goes fishing. This is obviously suggestive of Simon Peter, the "fisher of men."

There's also a theme of some kind of Trinity with Perceval and the Fisher King. Three things are displayed before Perceval, a sword, a lance and the Grail. Perceval must see the Fisher King three times before he can be bequeathed the Grail.

The references to fertility / infertility are also there; the Fisher King himself says that he cannot get up to meet Perceval. It is said that he cannot mount a horse. The injuries would suggest that he has likely been rendered infertile. The phallic imagery of the bleeding lance and the broken / mended sword, and the fecundity of the Grail (Perceval lives from nothing but the produce of the Grail for seven years at the end of the poem), all hint at a lineage in crisis that must be repaired through some kind of holy mysticism. As it happens, Perceval is related to the Fisher King, but he must earn his right to that lineage through good deeds and renunciation of sin. So, you could argue that the allusion to Peter is there again, the Fisher King is the start of the new holy lineage (the rock, or start of the church), and admission to the line of Peter (the papacy) may be earned through a virtuous life.

Eschenbach embellishes a little more a few years later. Mallory then picks these bare bones up and adds in more details in Le Morte d'Arthur but I don't have a copy of those to hand. Interestingly, as I remember Mallory, it was an attempt to write a kind of "history," whereas Perceval reads as a list of symbols and metaphors at times.

I think it's safe to say he was of some significance to medieval writers; firstly, the idea of the Grail was given an actual corporeal form and location in the story of the Fisher King. It makes it attainable. Secondly, it reinforces ideas of bestowed lineage. The Fisher King was most recent member of the Grail lineage. You can only join this lineage if you're noble and free of sin. Tying the idea of divinity, or at least divine approval into ideas of inheritance of power etc. would presumably have been a powerful way to bolster support for the status quo.

Source: Chretien de Troyes "Perceval", Boydell & Brewer 1996 (Nigel Bryant Translation).

What do you mean? Who is the historical person, if any, on whom the Fisher King story is based? Or do you want a literary history of the story itself?

Reading up on the Fisher King and his background on Wikipedia, I see a common theme was the "healing question" that needed to be asked to heal his wound and by extension his lands. However, I can't find what this question actually was. What was the healing question?