I believe Savage Worlds and Hellfrost meets most of your requirements. Although it is classless, Hellfrost has multiple ways in which it encourages and supports the playing of a noble character, and I would encourage you to consider it even though classes themselves are not supported. In part this is built into the background information for the setting, but there are also specific rules and mechanics for how nobles interact with the world and other characters.
The class should model a noble from level1 as it were, no at level 10 you gain a castle and followers.
Nobles are allowable at a variety of different ranks, and this varies further depending on the realm you live in and your race. There is a lot of background information to give you plot hooks for this kind of thing should you need them.
The system also has additional rules for governing a resource such as a castle (although these are not in the main Hellfrost books and have to be bought seperately), breaking down its management by season and generating interesting events that you might have to deal with. There are multiple ways to gain followers although you have to work out exactly how you are going to pay their wages, and the elegance of the system means that having these followers does not significantly slow down the game.
It should be noted though that a large part of the journey from a 'low' to 'high' level noble will be down to your GM, as they have to fill in the details of how you go through that progression depending on the adventures your character participates in.
The class should have explicit rules for interacting with non combat social challenges
Savage Worlds includes skills such as Persuasion, Intimidation, Taunting and Notice, the latter being used to 'read' people. There are also rules for 'social combat' used particularly for longer social arguments/discussions, and Dramatic Tasks, which can often be used for non combat scenarios. The rules for governing resources are also detailed enough to given you plenty of possible uses for non combat skills.
The class should have explicit rules for interacting with my party members/henchmen so that I make them fight better i.e my most potent ability is leadership
Savage Worlds and Hellfrost in particular contains a huge number of Leadership Edges that allow your character to directly influence the way in which your subordinate party members/henchmen fight etc, and range from simple things such as increasing their morale, to more complex matters such as coordinating ranged combat to have a better chance of taking down larger foes. This is one of the biggest strengths of the system in my opinion.
No class like a bard where I have to strip out all the musician flavour but then I'm still stuck with a noble who is very very good at singing despite having no reason to be that good
Being a noble does not have to have anything to do with singing :)
No classes that would derive their authority from supernatural powers playing sorcerer kings descended from the dragons is fun, but not related to this question
Although nobles can be magical, there is no requirement for this to be the case.