Can I add ash from my coal fire to my compost?(for wood stove ash follow this link, for BBQ ash follow this link)
DO NOT add hot ash to the HotBin, or any other compost bin - it will damage the plastic and void the warranty. It can ignite a fire if your heap is very dry
Can add the cold ash (ashes) from a coal fire to my compost?
Yes, but too much ash will turn the compost waste strongly alkaline and this will slow down the composting process. Ensure you mix the ash in with the other compost. Avoid adding one thick layer - this will form an impervious barrier and prevent airflow when it becomes wet. As a rule of thumb - if you are running a coal fire heating, you will porduce too much ash to add into a HOTBIN.
How beneficial is coal ash to the heap versus directly adding it to the soil?
Coal ash will not biodegrade ('breakdown' or compost). However the fine particles will be incorporated into your compost. Coal ash is a mixture of minerals including potash (ie potassium oxide), the source of the second item in NKP fertiliser list. Potash (like any fertiliser) has to be used sparingly. Spread 'thickly' around stems/roots it will 'burn' as it is highly alkaline - so there are some advantages of 'diluting' the potash into your compost.