SWORDSMANSHIP! I think Rand is naturally athletic and in shape from his youth and life as a farmhand. He learned the flame and the void from a secret blademaster in his father, Tam, throughout his youth and also is a genetic BEAST from his Aiel ancestry! Obviously training in between book 1 and book 2 with the most legendary Warder alive, Lan, doesn't hurt. But you know all this!
I feel like Robert Jordan made a nice little recipe for a young man with amazing natural ability to become a rapidly improving swordsman.
The way Rand Channels throughout all the books is very intuitive and often times out of his control and beyond his conscious knowledge, as Lews Therin reborn (madness included) , a man who also lived as blademaster for hundreds of years. So to say Rand is a "natural" is a pure understatement.
So if I disagree with anything, Lexi Eve, it's the idea that according to the story that Robert Jordan tells- Rand Althor should NOT be able to beat a blademaster by the end of book 2??
Rand is questioned about rockin' a heron mark blade from the beginning of book 1, only keeps the sword as a reminder of who his father is and pure stubborness, and is finally challenged by the end of book 2. All of these factors, combined with being the most powerful ta'veren of all time!
Now Matt Cauthon's ability with the Ashandarei, alongside his naturally ability with a quarterstaff! Matt's internal narrative and thoughts concede that he gained xp and skills from the memories of his past selves! His conscious memories from past lives are a tool that Jordan uses and admits are a part of that characters skillset, no need for speculation whatsoever.
As far as Rand becoming Lord, soldier, General, and King. These were all roles that Rand denied, fought and struggled against until he eventually accepted, mostly due to his solid upbringing and Lan's influence in developing a deeper sense of duty. At no point in the entire Wheel of Time series is it stated that Rand is GOOD at any of these things, King OR General. He's generally feared by most and hated by many, and never loved as a king or admired as a general. His skill with the blade or as a warrior might be the only thing he truly did excel at, and i'm not sure he ever even surpassed his father Tam, let alone Lan with the Blade. Shit, Galad, and even Gawn might've suprassed Rand's blade skills by the end of the last book ( one hand or both).