In MTW, troops that have the option to dismount will always start battles mounted, and you can dismount them at the start of every battle if you wish (and if you can; some troops, most knights, eg., can only dismount for sieges).
I think the Monastery guys have already answered your historical questions about Arthur and his knights; they may have been fictional/mythical, as he may have been, and what they were and how many there were depends on which period you think they or their legend originates from.
Nobles of most periods have been able to afford horses and better (or even just some!) armour, so I guess it is always likely that they fought mounted, armoured and possibly charging with lances or long spears. There are unlikely to have been many of them (probably not more than, say, 100; in the Roman army, cavalry were organised into turmae, troops, of 30 men, four of which made an ala, or 120 men, so if the Knights were Sarmatian auxiliaries or otherwise ex-Roman, they might have been around one of these numbers) as the population and economy of any period of British history from which they might have originated simply did not allow very large armies or a very advanced standard of equipment for large numbers of troops.
(The most likely theory I've come across for the 'Round Table' thing comes from the Celtic (and probably most tribal military units) tradition of a warrior band eating in a circle around a fire so that all can share food and warmth equally and pass things around, and take turns at telling tales and singing.)
EDIT: having read the other Knights of the Round Table thread; if they're a unit in BI or MTW2 I know nothing whatsoever about them or their characteristics; if your question was about that, ignore this post! (BTW, if so, you should've posted that stuff in the Main Hall or MTW2 forum anyway)
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