Having a .223 rifle does not necesarily mean you can't use 5.56mm ammo. A lot of people do and have no problems. If a problem occurs, it will most likely be a feeding or extraction problem.
The military uses M855/SS109 type ammunition in the 1/7 twist barrels. Yes, it is available for civilian sales.
The 6400 is one of the few Colts I would reccommend. It is the crown jewel in their civilian line-up. A Bushmaster would be the only real competition to the 6400, but the 6400 comes with a lot of features that would take extra money and effort to make a Bushy M4 similar.
Colts are pretty hard to find in most areas. Civilian sales are a low priority with Colt these days. The only real concern is the good possibility that Colt's customer service will be quite lacking in the case that you have a problem. That is not always the case, but sems to be a lot of the time. However, the good news is that the 6400 seems to be the model with the least problems in Colt's product line.