Hard to know where to begin with this. Ultimately, all those questions boil down to what you want to happen in your campaign. Do you want the characters embroiled in local battles and war? Are they likely to be involved in trade? If there's disease afflicting the land, then you'd have to decide who gets it, what the response is, and (perhaps) roll to see if the characters are affected. It's up to you whether all these things are a 'background' to your campaign or something the characters have to be actively involved in. It might also be a good idea to find out what your players want out of a game before you start...
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...but is there any medieval european examples?
Yes. Absolutely
lots. War was a favourite pastime of European nobles and one of the reasons commonly attributed to the Crusades was an opportunity to get those troublemakers out of the area. What tended to stop wars was an increased central authority (i.e. a strong Crown) and the slow realisation that war is bad for trade - a noble could easily win a local conflict and end up worse off financially.
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What effect does the crusades have on markets?
It makes items previously unheard of accessible in Coradian markets. Spices, silks, Ta'ashim horses (amongst other things) all become available. The building of castles is vastly improved as military science is given a boost - whether any character would note this in your games is up to you.
A local war, in contrast, stifles trade. Availability of all goods that are not locally produced staples is likely to drop significantly and prices would rise in that area. For characters, inn prices are likely to rise (double or more), and availability of items for purchase is likely to drop (at your discretion). Of course, this could lead to characters trying to 'cash in' by selling their items, but such activity can easily lead them to falling foul of the local market rules and getting into trouble with the local lord...
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What if everyone warred with Chaubrette?
Why would they? The concept of 'nation' really belongs to the post-medieval age. Prior to that, wars are fought between lords (and kings). A war against Chaubrette would really be a war against the king of Chaubrette...
(And, with Chaubrette being situated where it is, such a war would have a massive adverse impact on trade in the area.)