I don't know much (and nothing firsthand) about the .223WSSM, but from what I've read I can't see much reason to get it rather than a 22-250, or 220 Swift. I really don't see how the savings of a half inch or so on action length would really matter. I mean, seriously, would you choose an overall 39.5" rifle over a 40.0" rifle? The shorter action does not, from all accounts I've seen, offer any improvement in real world accuracy. If you don't already have any .22 centerfires, then a .223WSSM might make sense. But doubt I'd ever trade a 22-250 or 220 Swift on one.
Feeding and extraction are not likely to be an issue with a bolt gun, or least no more of an issue than with any other caliber in that rifle. I think there were some problems with that on the early test rifles, but I would imagine they've licked any that were there by now. The rifles featured in the few articles I've seen on the cartridge have all been bolt actions, though if it's properly designed an autoloader should work OK.
As long as the brass is boxer primed, and it is essentially guaranteed to be so primed, then it will be reloadable. Brass life probably won't be as long as with non-magnum .243 though.
At least in terms of the .243WSSM, what I've been seeing is that it really doesn't buy you anything in terms of performance over the 6mm Rem cartridge. And, with it's higher powder capacity it will burn out barrels faster than the 6mm. The .240 Weatherby Mag does actually give a performance advantage though.
http://www.chuckhawks.com/243wssm.htm
If you choose to subscribe you can view the entire article, rather than the exerpt above. In it he lists a factory load of a 100 grain bullet at a 3110 fps MV. For the 6mm, the 100 grain factory loads are listed at 3100 fps. That's a meaningless difference.