After reading various post about carrier bearings, it is my assumption that the carrier bearing should have no play(mine does). Is this a correct statement?

Also, there is some question as to weather this little gem has to be pressed off and on? I have seen it posted both ways. Is it possible to disconnect one side only then slide the thing off and slide the new one on?

This is a 4 wheel drive dually extended cab.

 

There should be no play, like any bearing, and for how expensive they are it's best to have a drive line shop press it on for you. It's easy to damage the thing trying to pound it into place. Just my $.02..

 

Took it apart...bearing is fine..the bushing is torn a little. Can I drive it like that?

 

By bushing do you mean the rubber shock mount surrounding the bearing? You can drive for quite some time with the rubber shock mount compromized, as long as the drive lines are balanced fairly well and you down dump the clutch too much, but no matter how well the shafts are balanced you most likely will get some vibration from it.