My heat pump outside is iced over but fan still running. My furnace still kicks on but the thermastadt goes to EMERG. I have a work call in is it okay to run my furnace till they come look at it.

It might be a smart idea to turn off the power to the outside unit. There is usually a disconnect close to the unit outside that will turn it off. This way you will eliminate any possible further damage to the unit since if it freezes over enough to have ice stop the fan then fan motor damage could happen.

Will my furnace and hot water heater still work as normal? There was a switch outside by the unit so I turned it off.

The other items should work but your furnace will be running on resistance heat which will get you by.

This is the exact reason to use emergency heat. The HP is turned off and only the resistance elements are used. Heating is more expensive in this mode. It's basically like having an electric furnace.