Can I share the dishwasher or other appliance lines from adjacent room lines?
The most relevant NEC section is:


  210.23(A)(2) (2)Utilization Equipment Fastened in Place. The total rating of utilization equipment fastened in place, other than luminaires, shall not exceed 50 percent of the branch-circuit ampere rating where lighting units, cord-and-plug-connected utilization equipment not fastened in place, or both, are also supplied.


Roof icer plus dishwasher sounds like a bad combination.  Putting all your fixed items together (e.g. furnace) is reasonable.