I would purchase a basic "trouble-shooting" kit. This includes a temperature gauge, a set of sockets, and allen wrenches designed for Hvac units. Your AC manual has a bi-unit schematic.
For cleaning the coil it may require to cut the refrigerant line, remove the coil and other components for cleaning and then reinstall it, pull a vacuum on the refrigerant line and fill with refrigerant.
You are going to be able to use regular soap and water. Make sure you dont leave any water leftover. Let it air dry for about 3 hours before you reinstall the coil.
