Fumes from the inverter:
I don't expect any toxic fumes other than the "normal" smells of plastic, paint. However, under fault conditions there are often smells a bit like burning paint or plastic (which it probably is). The type of components that get overheated are resistors, wire (insulation), circuit boards, Transformers and power semiconductors. A place to check especially is the high current connections like where the battery cables are connected. If the joint is poor (loose) these can get very hot.
If you look inside (while it is properly disconnected) you would expect to see discolouration of the offending parts. A mild brown is probably an indication that it is hot, but maybe not excessively so, while black and charred should definitely not be. If you are really keen you could run the inverter and check hot spots with an infrared thermometer, remembering everything inside is electrically dangerous.
I would design to keep everything under 50C on a hot day, but not everyone comes from the tropics like I do. If parts are over 80C that is definitely too hot, as capacitors and other plastic, including PVC insulation are becoming "soft".
To solve the problem of why? Not easy unless it is overloaded. Sometimes resistors can get very hot in normal operation, and discolouring of parts close by is more or less expected. This is bad design. You could replace them with a resistor of the same value with a higher wattage rating, one with a metal skin and perhaps a small heatsink would help. An inverter could get overheated if its fan is restricted. If it doesn't have one it may not be continuously rated. A fan makes a very big difference to how well something cools.
The last issue is batteries. You say there are two? How big?Hydrogen and oxygen (extremely explosive) is generated as well as SO2 and SO3 fumes during overcharging. Overcharging should not happen, but I don't know what your charging arrangements are. The voltage should be close to 13.85V for float charging a 12V battery. If it is overcharging you lose too much electrolyte. Flooded electrolyte batteries should be kept outdoors and well ventilated. Larger sealed types (much bigger than a house brick) are better kept outside too. Hydrogen leaks through just about anything. Note the sealed (gel) types can quickly die in the sun from drying out.
I have seen a serious explosion with a car battery disintegrating into shrapnel from starting a vacuum cleaner in the same room about 20 feet away. It was being charged. I have also seen the results of a small SLA battery charged overnight in a sealed container with a switch. Next morning when turned on it exploded, driving the container downwards into the bench, and pushing windows and ceiling tiles out of their frames (and injuring the person who turned it on). In both these battery explosions shards passed through glass windows like bullets (leaving holes).
Death...!
Short term exposure to inhaling plastic fumes will not cause negative effects on a person's health. If the fumes are inhaled over long periods of time a medical evaluation should be done.
Yes, breathing in sulfur fumes can be harmful to your health. Sulfur fumes can cause irritation to the lungs, throat, and eyes, leading to symptoms such as coughing, shortness of breath, and eye irritation. Prolonged exposure to high levels of sulfur fumes can also cause more serious health effects.
Crude fumes are gases or vapors released through the burning or processing of crude oil. These fumes can contain harmful pollutants, such as volatile organic compounds and nitrogen oxides, which can contribute to air pollution and have negative health effects on humans and the environment.
Sulfuric acid fumes escaping from the battery.
The fumes are flammable just like gasoline fumes.
Oil fumes consist of volatile organic compounds (VOCs), particulate matter, and potentially toxic chemicals like benzene, toluene, and xylene. Inhaling these fumes can lead to respiratory irritation and long-term health effects. Proper ventilation and avoiding exposure are important to minimize the risks associated with oil fumes.
The battery will release sulfuric acid fumes that can be very toxic if inhaled. There will also be fumes from the burning plastic and other parts of the battery including lead. Burning a battery is a bad idea.
It's extremely explosive and is also dangerous to breath. The sulfuric acid in the battery will be trapped in the fumes as droplets. This is very hazardous to your health. It is also known as Hydrogen Sulfate.
No, but fumes from the battery acid can ignite with a spark.
Sulfuric acid fumes escaping from the battery causes this corrosion.
Yes, a a battery will emit the fumes from the Sulfuric acid which is extremely toxic.