Are split receptacles wired with #14 appropriate in a bedroom?
That is totally fine.  NEC requires receptacles be at a certain spacing (so extension cords are not needed).  It does not care if those receptacles are split and half controlled by a light switch.  

If anything, split receptacles all around help avoid the need for extension cords.  I see many homes where the solitary split receptacle is stupidly placed, and you are stuck with a bad placement, or must run an extension cord.  

You need to be very careful with splitting receptacles.  You must break off the correct tabs.  If you fail to break off a tab that needed to be broken, you will cross circuits into each other, defeat light switches, or make a rather big bang if it's an MWBC.  If you break off one too many tabs, one outlet won't work.  If it's getting confusing, then break off both tabs and pigtail both sides of the receptacle, and hook them up as if they are 2 separate receptacles, one at a time. 

If another bedroom has 2 complete circuits for bedroom receptacles, that is fine.   It would be rather unusual to see a receptacle split between two different circuits, but this is a rarely-seen feature, not a bug. 

It's also possible that a duplex receptacle, or even a receptacle chain, could be fed by a multi-wire branch circuit.  This carries 2 full circuits on a single /3 cable (black red white).  These are very efficient ways to bring a lot of power to a room, if you know what you're doing.   If you don't, you can inadvertently create a serious hazard.  This MWBC solution would not be used in new work, because it makes AFCI and GFCI protection more expensive, it is cheaper to simply run two separate /2 cables.