> but what the hell was with the girl that could repel bullets but it turns out that it was magnets but actually maybe she does have powers?

MGS always rides the line between "it's actually just tecnology" and "no, it was really supernatural." This is true of Psycho Mantis in MGS1 as well, and The Sorrow in MGS3 is literally a ghost. I assume that Kojima has read up on the Stargate Project and other psychic soldier projects and likes to think about "what if one of those bore fruit?" Anyway, in the context of Fortune, it's a dramatic take on that: her powers were actually a magnetic device planted on her by The Patriots, but ACTUALLY actually she really does have some psychic ability which allows her to fight Ocelot in her final moments.

> And what about the weird thing where you start sword fighting your father/president/clone?

Well, that's actually pretty straightforward. You fought Solidus Snake, who was the third clone of Big Boss, and the "main antagonist" of the game (scare quotes because arguably the Patriots are the real antagonists). At the end of the game, it is revealed that Raiden's girlfriend Rosemary is a) real, b) alive, c) pregnant and d) being held captive by the Patriots, and they task Raiden with killing Solidus if he ever wants to see her again. Why a sword fight? I dunno, some things we must simply chalk up to "because it's cool."

If you want to dive further into who Solidus was, yes, he was also a pseudo-father to Raiden, in the sense that Raiden was raised as a child soldier and Solidus was (at the time) his commander. Solidus was President during the events of MGS1 under the name George Sears, but by MGS2 he's leading the Sons of Liberty as part of his anti-Patriots plot. Unfortunately, Ocelot is still working as a Patriots double-agent at this point, and Raiden's involvement is in turn orchestrated by the Patriots, so it doesn't quite work and the whole operation is manipulated from the start.