If we are to believe the total hardness, then your hardness would only be 5.3 grains. Most water departments report an average, and you want the worst case. Suppose 9 months of the year, they pull the water from a river, and 3 months of the year they pull the water from a well. River water tends to be less hard, and well water is significantly harder.
1. If I assume 10 grains, then 1.5 cuft of resin in a 10x54 inch tank is plenty.
You must insist on 10% crosslinked resin, unless you have that carbon tank before the softener.
2. Downflow is more foolproof.
3. Carbon tanks don't have a meter, but it is better if they have a backwashing valve atop the tank. If there is not a big thing up there that looks about the same as for a softener, that would be upflow carbon tank. That risks getting the media clumped together. Carbon can both remove chlorine/chloromine, but also organic chemicals.
4. Probably. This assumes you have at least 40 psi of water pressure.