Why do the warning signal lights constantly stay on inside the dashboard?

Hello, warning lights and hot air coming out are very likely not related. It sounds like you have more than one problem going on with your Honda. First, with warning lights, a good diagnostic tool with power train, body and chassis code pulling and component monitoring capability will be needed to determine what clues you have that are turning the lights on. Find a locally qualified technician near you that can help here. Regarding the air concern: Air conditioning problems can originate by one of the following general areas: 1) A problem with the refrigerant system. Meaning, the refrigerant used has escaped and there is not sufficient refrigerant to pressurize the system properly, resulting in hot air. When this happens, the system must be checked for leaks, the leaks repaired, and the system recharged. 2) A problem mechanically or electrically with the under hood components. If the compressor has failed, it will not allow the system to operate. Further, if the system becomes contaminated with debris from a failed compressor, this can be even worse. Electrically, the coil of the compressor may not be working properly, or a cycle switch could fail preventing the system from operating. If your condenser fan is not working, the system may not work properly also. 3) Climate control problem inside the vehicle. If the system that operates the heating, ventilation and air conditioning system fails to operate properly, then the under hood components may not be turned on or off properly, keeping the cold air from being produced. Only testing these systems will yield a direction and an eventual result. Here are some shops near you: https://repairpal.com/repair-shops/honda-repair-and-service-in-chester-virginia