There is no absolute reason why it's better to round the back of a bow, or the belly for that matter. It's mainly a stylistic thing, or dealing with the natural crown of a narrow tree stave. You can go deeper into it, reasons like trapping, or crowned staves, and wood usually being stronger in tension than compression, theoretically advantages performance in some designs.
You can tiller the whole belly including the handle if necessary. It depends on the dimensions of the stave you start floor tillering, and the weight of the bow you intend. Unless you are familiar with the design, and species you might not have a good idea of how thick to go. In this case it's better to go with a thicker handle than necessary and tiller bend into the handle area later in the process. Have the handle bending too early and what usually happens later on is this section bends too much through the handle, and not evenly enough in the limbs, when you reach your intended draw length.
If you start with known dimensions of a bow that bends through the handle with a good tiller, you probably won't need to remove much wood if any from the handle area.
