Historically after 1066 yes, but they wouldn't before that or if the Norman invasion didn't happen and they wouldn't also speak Italian, Lithuanian, Persian, German and Greek etc. Which is the point I was making in that sending someone off to anywhere in the world which you can do currently in CK2 doesn't make sense realistically.
All of whom are untrusted random people. Finding someone you can trust who speaks the native language, familiar with the place and is willing to be part of your plan I would argue would actually not be easy.
There were actually a ton of French speakers running around England long before the Norman conquest, just due to the proximity. They intermarried regularly, and the trade potential (it was probably cheaper for a merchant in London to trade with one in Normandy or Flanders than it would be to trade with someone in northern England) meant that there was plenty of commerce. The converse is also true.
As for more exotic languages, those happened less frequently, but still relatively frequently. A merchant will need to be able to interact with their partners, and a merchant in a major trading hub could have partners all sorts of places (and if they didn't they would likely know people who would). You'd be relying on these sorts of connections to evaluate people ("Bob knows that Alice is trustworthy, and Alice recommends Carol as someone loyal and familiar with Greek merchants, who in turn recommends David as someone who will be reliable, amenable and able to go to Constantinople without suspicion"). Which is pretty much what any plotter would do anywhere (it's not like you can put up a poster saying "anyone interested in helping me kill my brother, please send your CV to this address" for a domestic killing either).
So a trusted courtier then. Again my whole argument is that it would be unlikely that the court would be full of people who knew about and spoke the language of all the various parts of the world to be able to plot anywhere and everywhere. A distance modifier if no hard limit would potentially make this a little more realistic. So an English noble plotting against immediate neighbours in the British Isles and intermediate neighbours in France, Ireland etc. would be easier than trying to plot against an Indian Rajah. Whom it is likely that only a handful of people in the realm are even aware of them.
I'd be happy with the plotting range being simultaneous with the diplomatic range. It's easier and more intuitive from a user perspective.
Not likely to inherit but still part of the royal family all the same. Only someone with wealth or prestige can just wander around Europe being hosted. Would a Lithuanian count agree to host some random nobody count from Scotland? Hosting a member of the English royal family is more of an honour and you know the guest, or their family, has the means to repay you with coin or favour.
Sure, but a somewhat remote one (a cousin of the king, and not one on good terms with said king even before he was exiled) and more known for his own wealth/valor. There were plenty of perfectly reasonable reasons for someone to be traveling long distances (pilgrimages or crusades being examples where hosting even a relatively unknown would be somewhat prestigious in its own right, as long as they were sufficiently wealthy that you could be reasonably sure they wouldn't steal your silverware). And a merchant could, of course, go almost anywhere.
I agree though that exiles dreaming of home and foreign soldiers would definitely have an interest in joining a plot to right the wrong that lead to them being exiled. I guess that is what the game tries to simulate with inviting someone to your court with a claim. A better use of that system to generate plots would be welcomed. Again though I believe that would tie into distance as I would assume that there weren't many Russian exiles in Spain or Greeks in Scotland. These peoples would tend to gravitate to somewhere where they could return to their homeland fairly easily and to somewhere where you may be able to hitch your claims to your new liege's desires. Thinking the French kings supporting Scots and exiled English royalty. There will likely be many historical instances of long distance exiles but those are notable exceptions.
Apologies for length, again
No need to apologize for length; it would be somewhat hypocritical for me to complain, after all
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Foreign soldiers popped up everywhere; the advantage of a foreign mercenary in your employ is that he's much less likely to have domestic connections that encourage him to play politics or have loyalty to domestic enemies (the Duke of Such-and-Such a place may have qualms if you ask him to fight his rebellious cousin, but some random foreigner won't care). The Varangians, Franks and later Catalans/Navarrese in Greece, the Normans in Sicily, literally everybody in Italy (English, French, German, Hungarian, etc. all had their own companies, stereotypes and rivalries as mercenaries in Italy, with the availability fluctuating as wars/crises in the home country drew people back). Plenty of these become permanent fixtures in a city (e.g. Milan may keep Mercenary Mike on retainer in their city if he's proven useful, rather than have to scramble to hire new soldiers whenever they need them), and will also likely sponsor many of their countrymen into their new homes (so, Mercenary Mike may offer a job in his company to promising Newbie Ned from his hometown).
Exiles are a bit more complicated (and dependent on political concerns, as a host country may decide the diplomatic hit of taking them in was too much and turn them out without warning). A lot of them eventually end up as mercenaries somewhere, and thus end up joining the general flow of folks around the continent whenever mercenaries are needed.